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  Jeroen Lamb  
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  Dmitry Turaev  
  Sebastian van Strien  
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Mike Field
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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
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Infinite-dimensional systems
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Nonautonomous dynamical systems
Pattern formation
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Chaos

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
  • Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle. DynamIC Preprint 2016-6
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
  • 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
  • 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
2015
  • 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
  • Tiago Pereira and Dmitry Turaev, Fast Fermi acceleration and entropy growth, Mathematical Modelling of Natural Phenomena 10, 3 (2015), 31−47. Article MathSciNet Preprint
  • Tiago Pereira and Dmitry Turaev, Exponential energy growth in adiabatically changing Hamiltonian systems, Physical Review E 91, 1 (2015), 010910(R), 4. Article MathSciNet Preprint
  • Kushal Shah, Vassili Gelfreich, Vered Rom-Kedar, and Dmitry Turaev, Leaky Fermi accelerators, Physical Review E 91, 6 (2015), 062920, 7. Article 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
  • 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
  • Dmitry Turaev, Christopher Warner, and Sergey Zelik, Energy growth for a nonlinear oscillator coupled to a monochromatic wave, Regular and Chaotic Dynamics 19, 4 (2014), 513−522. 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
  • Vassili Gelfreich, Vered Rom-Kedar, and Dmitry Turaev, Fermi acceleration and adiabatic invariants for non-autonomous billiards, Chaos. An Interdisciplinary Journal of Nonlinear Science 22, 3 (2012), 033116, 21. Article MathSciNet Preprint
  • 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
  • Vered Rom-Kedar and Dmitry Turaev, Billiards: a singular perturbation limit of smooth Hamiltonian flows, Chaos. An Interdisciplinary Journal of Nonlinear Science 22, 2 (2012), 026102, 21. Article MathSciNet Preprint
2011
  • Gheorghe Tigan and Dmitry Turaev, Analytical search for homoclinic bifurcations in the Shimizu-Morioka model, Physica D 240, 12 (2011), 985−989. 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
  • Vered Rom-Kedar and Dmitry Turaev, The symmetric parabolic resonance, Nonlinearity 23, 6 (2010), 1325−1351. Article MathSciNet
  • Kushal Shah, Dmitry Turaev, and Vered Rom-Kedar, Exponential energy growth in a Fermi accelerator, Physical Review E 81, 5 (2010), 056205, 6. 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
  • Dmitry Turaev and Sergey Zelik, Analytical proof of space-time chaos in Ginzburg-Landau equations, Discrete and Continuous Dynamical Systems A 28, 4 (2010), 1713−1751. Article MathSciNet
2009
  • Sergey V. Gonchenko, Leonid P. Shilnikov, and Dmitry Turaev, On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors, Regular and Chaotic Dynamics 14, 1 (2009), 137−147. Article MathSciNet
2008
  • Vassili Gelfreich and Dmitry Turaev, Unbounded energy growth in Hamiltonian systems with a slowly varying parameter, Communications in Mathematical Physics 283, 3 (2008), 769−794. Article MathSciNet
  • Vassili Gelfreich and Dmitry Turaev, Fermi acceleration in non-autonomous billiards, Journal of Physics A 41, 21 (2008), 212003, 6. 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
  • Anna Rapoport, Vered Rom-Kedar, and Dmitry Turaev, Stability in high dimensional steep repelling potentials, Communications in Mathematical Physics 279, 2 (2008), 497−534. 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
  • Anna Rapoport, Vered Rom-Kedar, and Dmitry Turaev, Approximating multi-dimensional Hamiltonian flows by billiards, Communications in Mathematical Physics 272, 3 (2007), 567−600. 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
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
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
  • Sam Gratrix and John N. Elgin, Pointwise dimensions of the Lorenz attractor, Physical Review Letters 92, 1 (2004), 014101, 4. Article 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
  • Stefano Luzzatto and Marcelo Viana, Exclusions of parameter values in Hénon-type systems, Rossiĭskaya Akademiya Nauk. Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk 58, 6(354) (2003), 3−44. Article MathSciNet
  • Jaroslav Stark and Kate Hardy, Chaos: Useful at Last, Science 301(2003), 1192−1193.
  • 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 Vered Rom-Kedar, Soft billiards with corners, Journal of Statistical Physics 112, 3−4 (2003), 765−813. 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
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
  • Vered Rom-Kedar and Dmitry Turaev, Big islands in dispersing billiard-like potentials, Physica D 130, 3−4 (1999), 187−210. Article 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 Vered Rom-Kedar, On smooth Hamiltonian flows limited to ergodic billiards, in: Chaos, kinetics and nonlinear dynamics in fluids and plasmas (Carry-Le Rouet, 1997), Lecture Notes in Phyics, 17−50, Springer, Berlin, 1998. Article MathSciNet
  • Dmitry Turaev and Vered Rom-Kedar, Elliptic islands appearing in near-ergodic flows, Nonlinearity 11, 3 (1998), 575−600. 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
  • 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
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
1989
  • Vladimir M. Eleonskiĭ, Nikolai E. Kulagin, Dmitry Turaev, and Leonid P. Shilnikov, Classification of self-localized states of an electromagnetic field in a nonlinear medium, Doklady Akademii Nauk SSSR 309, 4 (1989), 848−852. MathSciNet
  • Dmitry Turaev and Leonid P. Shilnikov, Hamiltonian systems with homoclinic saddle curves, Doklady Akademii Nauk SSSR 304, 4 (1989), 811−814. 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
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