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STAFF
  Jeroen Lamb  
  Martin Rasmussen  
  Dmitry Turaev  
  Sebastian van Strien  
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Mike Field
POSTDOCS
Fabrizio Bianchi
Trevor Clark
Nikos Karaliolios
Dongchen Li
Paul Verschueren
Björn Winckler
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Alex Athorne
Sajjad Bakrani Balani
Giulia Carigi
Andrew Clarke
Maximilian Engel
Federico Graceffa
Michael Hartl
Giuseppe Malavolta
Guillermo Olicón Méndez
Cezary Olszowiec
Christian Pangerl
Matteo Tanzi
Kalle Timperi
VISITORS
Shangzhi Li
Ole Peters
Camille Poignard
Cristina Sargent
Bill Speares
Kevin Webster
RELATED STAFF
Mauricio Barahona
Davoud Cheraghi
Martin Hairer
Darryl Holm
Xue-Mei Li
Greg Pavliotis


PUBLICATIONS




Complete List

BY SUBJECT
Attractors
Bifurcation Theory
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Bifurcation theory

Preprints
  • Thai Son Doan, Maximilian Engel, Jeroen S.W. Lamb, and Martin Rasmussen, Hopf bifurcation with additive noise. DynamIC Preprint 2017-2
  • Jürgen Knobloch, Jeroen S. W. Lamb, and Kevin N. Webster, Shift dynamics near non-elementary T-points with real eigenvalues, to appear in: Journal of Difference Equations and Applications. DynamIC Preprint 2017-1
  • Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle. DynamIC Preprint 2016-6
  • Dongchen Li, Homoclinic Bifurcations that Give Rise to Heterodimensional Cycles near A Saddle-Focus Equilibrium. DynamIC Preprint 2016-3
  • Jan Philipp Pade and Tiago Pereira, Improving the network structure can lead to functional failures. DynamIC Preprint 2014-6
  • Mark Callaway, Thai Son Doan, Jeroen S. W. Lamb, and Martin Rasmussen, The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise. DynamIC Preprint 2013-4
2017
  • Masayuki Asaoka, Katsutoshi Shinohara, and Dmitry Turaev, Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics, Mathematische Annalen 368, 3−4 (2017), 1277−1309. Article MathSciNet
  • Deniz Eroglu, Jeroen S.W. Lamb, and Tiago Pereira, Synchronisation of chaos and its applications, Contemporary Physics 58, 3 (2017), 207−243. Article
  • Alexander S. Gonchenko, Sergey V. Gonchenko, Alexey O. Kazakov, and Dmitry Turaev, On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators, Physica D 350(2017), 45−57. Article MathSciNet
  • Dongchen Li and Dmitry Turaev, Existence of heterodimensional cycles near Shilnikov loops in systems with a $\BbbZ_2$ symmetry, Discrete and Continuous Dynamical Systems A 37, 8 (2017), 4399−4437. Article MathSciNet Preprint
  • Ivan I. Ovsyannikov and Dmitry Turaev, Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model, Nonlinearity 30, 1 (2017), 115−137. Article MathSciNet
2016
  • Fabio Bagarello, Anna Maria Cherubini, and Francesco Oliveri, An operatorial description of desertification, SIAM Journal on Applied Mathematics 76, 2 (2016), 479−499. Article MathSciNet
  • William Giles, Jeroen S.W. Lamb, and Dmitry Turaev, On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems, Nonlinearity 29, 10 (2016), 3148−3173. Article MathSciNet
2015
  • Vasso Anagnostopoulou, Tobias Jäger, and Gerhard Keller, A model for the nonautonomous Hopf bifurcation, Nonlinearity 28, 7 (2015), 2587−2616. MathSciNet Preprint
  • Henk Bruin and Sebastian van Strien, Monotonicity of entropy for real multimodal maps, Journal of the American Mathematical Society 28, 1 (2015), 1−61. Article MathSciNet
  • Thai Son Doan, Martin Rasmussen, and Peter E. Kloeden, The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor, Discrete and Continuous Dynamical Systems B 20, 3 (2015), 875−887. Article MathSciNet Preprint
  • Boumediene Hamzi, Jeroen S. W. Lamb, and Debra Lewis, A characterization of normal forms for control systems, Journal of Dynamical and Control Systems 21, 2 (2015), 273−284. Article MathSciNet
  • Jeroen S. W. Lamb, Martin Rasmussen, and Christian S. Rodrigues, Topological bifurcations of minimal invariant sets for set-valued dynamical systems, Proceedings of the American Mathematical Society 143, 9 (2015), 3927−3937. Article MathSciNet Preprint
  • Ivan I. Ovsyannikov, Dmitry Turaev, and Sergey Zelik, Bifurcation to chaos in the complex Ginzburg-Landau equation with large third-order dispersion, Modelirovanie i Analiz Informatsionnykh Sistem. Modeling and Analysis of Information Systems 22, 3 (2015), 327−336. Article MathSciNet Preprint
  • Lasse Rempe-Gillen and Sebastian van Strien, Density of hyperbolicity for classes of real transcendental entire functions and circle maps, Duke Mathematical Journal 164, 6 (2015), 1079−1137. Article MathSciNet
  • Jake Stroud, Mauricio Barahona, and Tiago Pereira, Dynamics of cluster synchronisation in modular networks: implications for structural and functional networks, in: Applications of chaos and nonlinear dynamics in science and engineering, Understanding Complex Systems, 107−130, Springer, Cham, 2015. MathSciNet Preprint
  • Dmitry Turaev, Maps close to identity and universal maps in the Newhouse domain, Communications in Mathematical Physics 335, 3 (2015), 1235−1277. Article MathSciNet Preprint
2014
  • Valentin S. Afraimovich, Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, and Dmitry Turaev, Scientific heritage of L. P. Shilnikov, Regular and Chaotic Dynamics 19, 4 (2014), 435−460. Article MathSciNet
  • Alexander Gonchenko, Sergey V. Gonchenko, Alexey Kazakov, and Dmitry Turaev, Simple scenarios of onset of chaos in three-dimensional maps, International Journal of Bifurcation and Chaos 24, 8 (2014), 1440005, 25. Article MathSciNet Preprint
  • Serey V. Gonchenko, Olga V. Gordeeva, Valery I. Lukyanov, and Ivan I. Ovsyannikov, On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node, Regular and Chaotic Dynamics 19, 4 (2014), 461−473. Article MathSciNet
  • Sergey V. Gonchenko, Jeroen S. W. Lamb, Isabel Rios, and Dmitry Turaev, Attractors and repellers in the neighborhood of elliptic points of reversible systems, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 454, 4 (2014), 375−378. MathSciNet
  • Sergey V. Gonchenko, Ivan I. Ovsyannikov, and Joan C. Tatjer, Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points, Regular and Chaotic Dynamics 19, 4 (2014), 495−505. Article MathSciNet
  • Leonid Pavlovich Shilnikov, Andrey L. Shilnikov, and Dmitry V. Turaev, Showcase of blue sky catastrophes, International Journal of Bifurcation and Chaos 24, 8 (2014), 1440003, 10. Article MathSciNet Preprint
  • Dmitry Turaev, Hyperbolic sets near homoclinic loops to a saddle for systems with a first integral, Regular and Chaotic Dynamics 19, 6 (2014), 681−693. Article MathSciNet Preprint
  • Yong Zou, Tiago Pereira, Michael Small, Zonghua Liu, and Jürgen Kurths, Basin of attraction determines hysteresis in explosive synchronization, Physical Review Letters 112(2014), 114102. Article
2013
  • Henk Bruin and Sebastian van Strien, On the structure of isentropes of polynomial maps, Dynamical Systems 28, 3 (2013), 381−392. Article MathSciNet
  • Sergey V. Gonchenko, Alexander S. Gonchenko, Ivan I. Ovsyannikov, and Dmitry Turaev, Examples of Lorenz-like attractors in Hénon-like maps, Mathematical Modelling of Natural Phenomena 8, 5 (2013), 48−70. Article MathSciNet
  • Sergey V. Gonchenko and Ivan I. Ovsyannikov, On global bifurcations of three-dimensional diffeomorphisms leading to Lorenz-like attractors, Mathematical Modelling of Natural Phenomena 8, 5 (2013), 71−83. Article MathSciNet
  • Peter E. Kloeden, Christian Pötzsche, and Martin Rasmussen, Discrete-time nonautonomous dynamical systems, in: Stability and bifurcation theory for non-autonomous differential equations, Lecture Notes in Mathematics, 35−102, Springer, Heidelberg, 2013. Article MathSciNet
2012
  • Vasso Anagnostopoulou and Tobias Jäger, Nonautonomous saddle-node bifurcations: random and deterministic forcing, Journal of Differential Equations 253, 2 (2012), 379−399. Article MathSciNet
  • Adriana Buică, Jaume Llibre, and Oleg Makarenkov, Bifurcations from nondegenerate families of periodic solutions in Lipschitz systems, Journal of Differential Equations 252, 6 (2012), 3899−3919. Article MathSciNet
  • Sergey V. Gonchenko, Ivan I. Ovsyannikov, and Dmitry Turaev, On the effect of invisibility of stable periodic orbits at homoclinic bifurcations, Physica D 241, 13 (2012), 1115−1122. Article MathSciNet
  • Lev M. Lerman and Dmitry Turaev, Breakdown of symmetry in reversible systems, Regular and Chaotic Dynamics 17, 3−4 (2012), 318−336. Article MathSciNet
  • Oleg Makarenkov and Jeroen S. W. Lamb, Dynamics and bifurcations of nonsmooth systems: a survey, Physica D 241, 22 (2012), 1826−1844. Article MathSciNet
2011
  • Ale Jan Homburg, Alice C. Jukes, Jürgen Knobloch, and Jeroen S. W. Lamb, Bifurcation from codimension one relative homoclinic cycles, Transactions of the American Mathematical Society 363, 11 (2011), 5663−5701. Article MathSciNet
  • Mikhail Kamenskii, Oleg Makarenkov, and Paolo Nistri, An alternative approach to study bifurcation from a limit cycle in periodically perturbed autonomous systems, Journal of Dynamics and Differential Equations 23, 3 (2011), 425−435. Article MathSciNet
  • Oleg Makarenkov, Luisa Malaguti, and Paolo Nistri, On the behavior of periodic solutions of planar autonomous Hamiltonian systems with multivalued periodic perturbations, Zeitschrift für Analysis und ihre Anwendungen 30, 2 (2011), 129−144. Article MathSciNet
  • Gheorghe Tigan and Dmitry Turaev, Analytical search for homoclinic bifurcations in the Shimizu-Morioka model, Physica D 240, 12 (2011), 985−989. Article MathSciNet
  • Dmitry Turaev, Diffeomorphisms which cannot be topologically conjugate to diffeomorphisms of a higher smoothness, Ergodic Theory and Dynamical Systems 31, 2 (2011), 563−569. Article MathSciNet
2010
  • Martin Rasmussen, Finite-time attractivity and bifurcation for nonautonomous differential equations, Differential Equations and Dynamical Systems 18, 1−2 (2010), 57−78. Article MathSciNet
  • Dmitry Turaev, Richness of chaos in the absolute Newhouse domain, in: Proceedings of the International Congress of Mathematicians. Volume III, 1804−1815, Hindustan Book Agency, New Delhi, 2010. MathSciNet
2009
  • Pietro-Luciano Buono, Martin Helmer, and Jeroen S. W. Lamb, On the zero set of G-equivariant maps, Mathematical Proceedings of the Cambridge Philosophical Society 147, 3 (2009), 735−755. Article MathSciNet
  • Shangjiang Guo, Jeroen S. W. Lamb, and Bob W. Rink, Branching patterns of wave trains in the FPU lattice, Nonlinearity 22, 2 (2009), 283−299. Article MathSciNet
2008
  • Robert E. Beardmore and Kevin N. Webster, Normal forms, quasi-invariant manifolds, and bifurcations of nonlinear difference-algebraic equations, SIAM Journal on Mathematical Analysis 40, 1 (2008), 413−441. Article MathSciNet
  • Robert E. Beardmore and Kevin N. Webster, A Hopf bifurcation theorem for singular differential-algebraic equations, Mathematics and Computers in Simulation 79, 4 (2008), 1383−1395. Article MathSciNet
  • Pietro-Luciano Buono, Jeroen S. W. Lamb, and R. Mark Roberts, Bifurcation and branching of equilibria in reversible-equivariant vector fields, Nonlinearity 21, 4 (2008), 625−660. Article MathSciNet
  • Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, On dynamical properties of multidimensional diffeomorphisms from Newhouse regions. I, Nonlinearity 21, 5 (2008), 923−972. Article MathSciNet
  • Shangjiang Guo and Jeroen S. W. Lamb, Equivariant Hopf bifurcation for neutral functional differential equations, Proceedings of the American Mathematical Society 136, 6 (2008), 2031−2041. Article MathSciNet
  • Ale Jan Homburg, Alice C. Jukes, Jürgen Knobloch, and Jeroen S. W. Lamb, Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows, Bulletin of the Belgian Mathematical Society. Simon Stevin 15, 5 (2008), 833−850. Article MathSciNet
  • Dmitry Turaev and Leonid P. Shilnikov, Pseudohyperbolicity and the problem of the periodic perturbation of Lorenz-type attractors, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 418, 1 (2008), 23−27. Article MathSciNet
2007
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps, Nonlinearity 20, 2 (2007), 241−275. Article MathSciNet
  • Jeroen S. W. Lamb and Ian Melbourne, Normal form theory for relative equilibria and relative periodic solutions, Transactions of the American Mathematical Society 359, 9 (2007), 4537−4556. Article MathSciNet
  • Martin Rasmussen, Nonautonomous bifurcation patterns for one-dimensional differential equations, Journal of Differential Equations 234, 1 (2007), 267−288. Article MathSciNet
  • Martin Rasmussen, Attractivity and bifurcation for nonautonomous dynamical systems, Lecture Notes in Mathematics 1907, Springer, Berlin, 2007. MathSciNet
2006
  • Ana Paula S. Dias and Jeroen S. W. Lamb, Local bifurcation in symmetric coupled cell networks: linear theory, Physica D 223, 1 (2006), 93−108. Article MathSciNet
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Homoclinic tangencies of arbitrary order in conservative two-dimensional mappings, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 407, 3 (2006), 299−303. MathSciNet
  • Ale Jan Homburg and Jeroen S. W. Lamb, Symmetric homoclinic tangles in reversible systems, Ergodic Theory and Dynamical Systems 26, 6 (2006), 1769−1789. Article MathSciNet
  • Martin Rasmussen, Towards a bifurcation theory for nonautonomous difference equations, Journal of Difference Equations and Applications 12, 3−4 (2006), 297−312. Article MathSciNet
2005
  • Claudio A. Buzzi and Jeroen S. W. Lamb, Reversible Hamiltonian Liapunov center theorem, Discrete and Continuous Dynamical Systems B 5, 1 (2005), 51−66. MathSciNet
  • Claudio A. Buzzi and Jeroen S. W. Lamb, Reversible equivariant Hopf bifurcation, Archive for Rational Mechanics and Analysis 175, 1 (2005), 39−84. Article MathSciNet
  • Sergey V. Gonchenko, Ivan I. Ovsyannikov, Carles Simó, and Dmitry Turaev, Three-dimensional Hénon-like maps and wild Lorenz-like attractors, International Journal of Bifurcation and Chaos 15, 11 (2005), 3493−3508. Article MathSciNet
  • Jeroen S. W. Lamb, Marco-Antonio Teixeira, and Kevin N. Webster, Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in R^3, Journal of Differential Equations 219, 1 (2005), 78−115. Article MathSciNet
  • Andrey Shilnikov, Leonid P. Shilnikov, and Dmitry Turaev, Blue-sky catastrophe in singularly perturbed systems, Moscow Mathematical Journal 5, 1 (2005), 269−282. MathSciNet
  • Dmitry Turaev, An example of a resonant homoclinic loop of infinite cyclicity, Moscow Mathematical Journal 5, 1 (2005), 283−293. MathSciNet
2004
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, The existence of a countable set of elliptic periodic trajectories in four-dimensional symplectic mappings with a homoclinic tangency, Trudy Matematicheskogo Instituta Imeni V. A. Steklova. Rossiĭskaya Akademiya Nauk 244, Din. Sist. i Smezhnye Vopr. Geom. (2004), 115−142. MathSciNet
  • Jeroen S. W. Lamb and Oleg V. Stenkin, Newhouse regions for reversible systems with infinitely many stable, unstable and elliptic periodic orbits, Nonlinearity 17, 4 (2004), 1217−1244. Article MathSciNet
  • Andrey Shilnikov, Leonid P. Shilnikov, and Dmitry Turaev, On some mathematical topics in classical synchronization. A tutorial, International Journal of Bifurcation and Chaos 14, 7 (2004), 2143−2160. Article MathSciNet
2003
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, On the dynamic properties of diffeomorphisms with homoclinic tangencies, Sovremennaya Matematika i ee Prilozheniya , 7 (2003), 91−117. MathSciNet
  • Igor Hoveijn, Jeroen S. W. Lamb, and R. Mark Roberts, Normal forms and unfoldings of linear systems in eigenspaces of (anti)-automorphisms of order two, Journal of Differential Equations 190, 1 (2003), 182−213. Article MathSciNet
  • Jeroen S. W. Lamb, Ian Melbourne, and Claudia Wulff, Bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactions, Journal of Differential Equations 191, 2 (2003), 377−407. Article MathSciNet
  • Dmitry Turaev, Polynomial approximations of symplectic dynamics and richness of chaos in non-hyperbolic area-preserving maps, Nonlinearity 16, 1 (2003), 123−135. Article MathSciNet
  • Dmitry Turaev and Sergey Zelik, Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations, Nonlinearity 16, 6 (2003), 2163−2198. Article MathSciNet
  • Kevin N. Webster and John N. Elgin, Asymptotic analysis of the Michelson system, Nonlinearity 16, 6 (2003), 2149−2162. Article MathSciNet
2001
  • Leonid P. Shilnikov, Andrey L. Shilnikov, Dmitry Turaev, and Leon O. Chua, Methods of qualitative theory in nonlinear dynamics. Part II, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises 5, World Scientific, River Edge, New Jersey, 2001. Article MathSciNet
  • Dmitry Turaev, Multi-pulse homoclinic loops in systems with a smooth first integral, in: Ergodic theory, analysis, and efficient simulation of dynamical systems, 691−716, Springer, Berlin, 2001. MathSciNet
  • Claudia Wulff, Jeroen S. W. Lamb, and Ian Melbourne, Bifurcation from relative periodic solutions, Ergodic Theory and Dynamical Systems 21, 2 (2001), 605−635. Article MathSciNet
2000
  • Jeroen S. W. Lamb, Ian Melbourne, and Claudia Wulff, Bifurcation from periodic and relative periodic solutions in equivariant dynamical systems, in: International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999), 175−185, World Scientific, River Edge, New Jersey, 2000. MathSciNet
  • Jeroen S. W. Lamb and Claudia Wulff, Pinning and locking of discrete waves, Physics Letters A 267, 2−3 (2000), 167−173. Article MathSciNet
  • Mikhail V. Shashkov and Dmitry Turaev, A proof of Shilnikov's theorem for C^1-smooth dynamical systems, in: Methods of qualitative theory of differential equations and related topics, American Mathematical Society Translations, Series 2, 149−163, American Mathematical Society, Providence, 2000. MathSciNet
  • Leonid P. Shilnikov and Dmitry V. Turaev, A new simple bifurcation of a periodic orbit of blue sky catastrophe type, in: Methods of qualitative theory of differential equations and related topics, American Mathematical Society Translations, Series 2, 165−188, American Mathematical Society, Providence, 2000. MathSciNet
1999
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Homoclinic tangencies of arbitrary order in Newhouse domains, in: Dynamical systems (Russian) (Moscow, 1998), Itogi Nauki Tekh. Ser. Sovrem. Mat. Prilozh. Temat. Obz., 69−128, Vseross. Inst. Nauchn. i Tekhn. Inform. (VINITI), Moscow, 1999. MathSciNet
  • Jeroen S. W. Lamb and Ian Melbourne, Bifurcation from discrete rotating waves, Archive for Rational Mechanics and Analysis 149, 3 (1999), 229−270. Article MathSciNet
  • Jeroen S. W. Lamb and Ian Melbourne, Bifurcation from periodic solutions with spatiotemporal symmetry, in: Pattern formation in continuous and coupled systems (Minneapolis, MN, IMA Vol. Math. Appl., 175−191, Springer, New York, 1999. Article MathSciNet
  • V. Pisarevskii, Andrey Shilnikov, and Dmitry Turaev, Asymptotic normal forms for equilibria with a triplet of zero characteristic exponents in systems with symmetry, in: Iteration theory (ECIT 96) (Urbino), Grazer Mathematische Berichte, 291−300, Karl-Franzens-Universität Graz, Graz, 1999. MathSciNet
  • Mikhail V. Shashkov and Dmitry Turaev, An existence theorem of smooth nonlocal center manifolds for systems close to a system with a homoclinic loop, Journal of Nonlinear Science 9, 5 (1999), 525−573. Article MathSciNet
1998
  • Leonid A. Bunimovich and Dmitry Turaev, Localized solutions in lattice systems and their bifurcations caused by spatial interactions, Nonlinearity 11, 6 (1998), 1539−1545. Article MathSciNet
  • Bernold Fiedler and Dmitry Turaev, Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions, Archive for Rational Mechanics and Analysis 145, 2 (1998), 129−159. Article MathSciNet
  • Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom, Regular and Chaotic Dynamics 3, 4 (1998), 3−26. Article MathSciNet
  • Jeroen S. W. Lamb, k-symmetry and return maps of spacetime symmetric flows, Nonlinearity 11, 3 (1998), 601−629. Article MathSciNet
  • Jeroen S. W. Lamb and John A. G. Roberts, Time-reversal symmetry in dynamical systems: a survey, Physica D 112, 1−2 (1998), 1−39. Article MathSciNet
  • V. Pisarevskii, Andrey Shilnikov, and Dmitry Turaev, Asymptotic normal forms for equilibria with a triplet of zero characteristic exponents in systems with symmetry, Regulyarnaya & Khaoticheskaya Dinamika. Regular & Chaotic Dynamics 3, 1 (1998), 19−27. MathSciNet
  • Leonid P. Shilnikov, Andrey L. Shilnikov, Dmitry V. Turaev, and Leon O. Chua, Methods of qualitative theory in nonlinear dynamics. Part I, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises 4, World Scientific, River Edge, New Jersey, 1998. Article MathSciNet
  • Dmitry Turaev and Leonid P. Shilnikov, An example of a wild strange attractor, Rossiĭskaya Akademiya Nauk. Matematicheskiĭ Sbornik 189, 2 (1998), 137−160. Article MathSciNet
1997
  • Sergey V. Gonchenko, Leonid P. Shilnikov, Oleg V. Stenkin, and Dmitry Turaev, Bifurcations of systems with structurally unstable homoclinic orbits and moduli of omega-equivalence, Computers & Mathematics with Applications 34, 2−4 (1997), 111−142. Article MathSciNet
  • Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, Quasiattractors and homoclinic tangencies, Computers & Mathematics with Applications 34, 2−4 (1997), 195−227. Article MathSciNet
  • Sergey V. Gonchenko, Dmitry Turaev, Pierre Gaspard, and Gregoire Nicolis, Complexity in the bifurcation structure of homoclinic loops to a saddle-focus, Nonlinearity 10, 2 (1997), 409−423. Article MathSciNet
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, On Newhouse domains of two-dimensional diffeomorphisms that are close to a diffeomorphism with a structurally unstable heteroclinic contour, Trudy Matematicheskogo Instituta Imeni V. A. Steklova. Rossiĭskaya Akademiya Nauk 216, Din. Sist. i Smezhnye Vopr. (1997), 76−125. MathSciNet
  • Leonid P. Shilnikov and Dmitry Turaev, Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries, Regulyarnaya & Khaoticheskaya Dinamika. Regular & Chaotic Dynamics 2, 3−4 (1997), 126−138. MathSciNet
  • Leonid P. Shilnikov and Dmitry Turaev, Simple bifurcations leading to hyperbolic attractors, Computers & Mathematics with Applications 34, 2−4 (1997), 173−193. Article MathSciNet
1996
  • Bernold Fiedler and Dmitry Turaev, Coalescence of reversible homoclinic orbits causes elliptic resonance, International Journal of Bifurcation and Chaos 6, 6 (1996), 1007−1027. Article MathSciNet
  • Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, Bifurcations of two-dimensional diffeomorphisms with non-rough homoclinic contours, Journal of Technical Physics 37, 3−4 (1996), 349−352. MathSciNet
  • Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits, Chaos 6, 1 (1996), 15−31. Article MathSciNet
  • Sergey V. Gonchenko, Oleg V. Stenkin, and Dmitry Turaev, Complexity of homoclinic bifurcations and $\Omega$-moduli, International Journal of Bifurcation and Chaos 6, 6 (1996), 969−989. Article MathSciNet
  • Jeroen S. W. Lamb, Local bifurcations in k-symmetric dynamical systems, Nonlinearity 9, 2 (1996), 537−557. Article MathSciNet
  • Mikhail V. Shashkov and Dmitry V. Turaev, On the complex bifurcation set for a system with simple dynamics, International Journal of Bifurcation and Chaos 6, 5 (1996), 949−968. Article MathSciNet
  • Dmitry Turaev, On dimension reduction near homoclinic and heteroclinic cycles, Journal of Technical Physics 37, 3−4 (1996), 437−440. MathSciNet
  • Dmitry Turaev, On dimension of non-local bifurcational problems, International Journal of Bifurcation and Chaos 6, 5 (1996), 919−948. Article MathSciNet
1995
  • Jeroen S. W. Lamb and Hans W. Capel, Local bifurcations on the plane with reversing point group symmetry, Chaos, Solitons and Fractals 5, 2 (1995), 271−293. Article MathSciNet
  • John A. G. Roberts and Jeroen S. W. Lamb, Self-similarity of period-doubling branching in 3-D reversible mappings, Physica D 82, 4 (1995), 317−332. Article MathSciNet
  • Dmitry Turaev and Leonid P. Shilnikov, Blue sky catastrophes, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 342, 5 (1995), 596−599. MathSciNet
1993
  • Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, On models with nonrough Poincaré homoclinic curves, Physica D 62, 1−4 (1993), 1−14. Article MathSciNet
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Dynamical phenomena in multidimensional systems with a structurally unstable homoclinic Poincaré curve, Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 330, 2 (1993), 144−147. MathSciNet
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, On the existence of Newhouse regions in a neighborhood of systems with a structurally unstable homoclinic Poincaré curve (the multidimensional case), Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk 329, 4 (1993), 404−407. MathSciNet
  • Andrey L. Shilnikov, Leonid P. Shilnikov, and Dmitry Turaev, Normal forms and Lorenz attractors, International Journal of Bifurcation and Chaos 3, 5 (1993), 1123−1139. Article MathSciNet
1992
  • Alexander S. Dmitriev, Yuri A. Komlev, and Dmitry Turaev, Bifurcation phenomena in the 1:1 resonant horn for the forced van der Pol-Duffing equation, International Journal of Bifurcation and Chaos 2, 1 (1992), 93−100. Article MathSciNet
  • Jeroen S. W. Lamb, The ferro-antiferro bifurcation transition in a microscopic model with incommensurate phases, Journal of Physics A 25(1992), 355−365.
1991
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, On models with a structurally unstable homoclinic Poincaré curve, in: Methods in qualitative theory and bifurcation theory (Russian), 36−61, Nizhegorod. Gos. Univ., Nizhniy Novgorod, 1991. MathSciNet
  • Sergey V. Gonchenko, Dmitry Turaev, and Leonid P. Shilnikov, Models with a structurally unstable homoclinic Poincaré curve, Doklady Akademii Nauk SSSR 320, 2 (1991), 269−272. MathSciNet
1989
  • Patrick Bonckaert, Freddy Dumortier, and Sebastian van Strien, Singularities of vector fields on R^3 determined by their first nonvanishing jet, Ergodic Theory and Dynamical Systems 9, 2 (1989), 281−308. Article MathSciNet
1988
  • Dmitry Turaev, Bifurcations of a homoclinic figure eight of a multidimensional saddle, Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk 43, 5(263) (1988), 223−224. Article MathSciNet
1987
  • Welington de Melo and Sebastian van Strien, Diffeomorphisms on surfaces with a finite number of moduli, Ergodic Theory and Dynamical Systems 7, 3 (1987), 415−462. Article MathSciNet
  • Sebastian van Strien, Normal hyperbolicity and linearisability, Inventiones Mathematicae 87, 2 (1987), 377−384. Article MathSciNet
  • Sebastian van Strien and Geovan Tavares dos Santos, Moduli of stability for germs of homogeneous vectorfields on R^3, Journal of Differential Equations 69, 1 (1987), 63−84. Article MathSciNet
1986
  • Dmitry Turaev and Leonid P. Shilnikov, Bifurcations of quasi-attractors of torus-chaos, in: Mathematical mechanisms of turbulence (Russian), 113−121, iii, Akad. Nauk Ukrain. SSR Inst. Mat., Kiev, 1986. MathSciNet
  • Dmitry Turaev and Leonid P. Shilnikov, Bifurcation of a homoclinic figure eight saddle with a negative saddle value, Doklady Akademii Nauk SSSR 290, 6 (1986), 1301−1304. MathSciNet
1985
  • Dmitry Turaev, Bifurcations of two-dimensional dynamical systems that are close to a system with two separatrix loops, Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk 40, 2(242) (1985), 203−204. MathSciNet
1984
  • Dmitry Turaev, A case of bifurcation from a contour formed by homoclinic curves emerging from a saddle, in: Methods of the qualitative theory of differential equations (Russian), 162−175, 203, Gorkov. Gos. Univ., Gorki, 1984. MathSciNet
1983
  • Henk Broer and Sebastian van Strien, Infinitely many moduli of strong stability in divergence free unfoldings of singularities of vector fields, in: Geometric dynamics, Lecture Notes in Mathematics, 39−59, Springer, Berlin, 1983. Article MathSciNet
1981
  • Welington de Melo, Jacob Palis, and Sebastian van Strien, Characterising diffeomorphisms with modulus of stability one, in: Dynamical systems and turbulence, Lecture Notes in Mathematics, 266−285, Springer, Berlin, 1981. MathSciNet
  • Sebastian van Strien, Saddle connections of arcs of diffeomorphisms: moduli of stability, in: Dynamical systems and turbulence, Lecture Notes in Mathematics, 352−365, Springer, Berlin, 1981. MathSciNet
  • Sebastian van Strien, On the bifurcations creating horseshoes, in: Dynamical systems and turbulence, Lecture Notes in Mathematics, 316−351, Springer, Berlin, 1981. MathSciNet