Home Publications Undergraduates Postgraduates Postdocs Calendar Contact

STAFF
  Jeroen Lamb  
  Martin Rasmussen  
  Dmitry Turaev  
  Sebastian van Strien  
RESEARCHERS
Mike Field
POSTDOCS
Fabrizio Bianchi
Trevor Clark
Nikos Karaliolios
Dongchen Li
Sofia Trejo Abad
Paul Verschueren
Björn Winckler
PHD STUDENTS
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
Cristina Sargent
Bill Speares
Kevin Webster
RELATED STAFF
Mauricio Barahona
Davoud Cheraghi
Darryl Holm
Greg Pavliotis


PUBLICATIONS




Complete List

BY SUBJECT
Attractors
Bifurcation Theory
Chaos
Computational dynamics
Ergodic theory
Game theory
Hamiltonian systems
Holomorphic dynamics
Homoclinic tangencies
Infinite-dimensional systems
Low-dimensional dynamical systems
Networks
Nonautonomous dynamical systems
Pattern formation
Random dynamical systems
Slow-fast systems
Symmetry
Tilings
Miscellaneous

Homoclinic tangencies

Preprints
  • 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
  • Dongchen Li, Homoclinic Bifurcations that Give Rise to Heterodimensional Cycles near A Saddle-Focus Equilibrium. DynamIC Preprint 2016-3
2017
  • 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
2015
  • 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
  • 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
  • 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, 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
2013
  • 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
2012
  • 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
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
  • 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
  • Vassili Gelfreich and Dmitry Turaev, Universal dynamics in a neighborhood of a generic elliptic periodic point, Regular and Chaotic Dynamics 15, 2−3 (2010), 159−164. 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
2008
  • 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
  • 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
2006
  • 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
2005
  • 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
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
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
  • 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
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
1998
  • 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
  • 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
1996
  • 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
  • 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
1994
  • Jeroen S. W. Lamb, Stochastic webs with fourfold rotation symmetry, in: Hamiltonian Mechanics: Integrability and Chaotic Behaviour, NATO ASI Series B, 345−352, Plenum, New York, 1994. 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
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