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

Attractors

Preprints
  • Nikolaos Karaliolios, Invariant Distributions and local theory of quasiperiodic cocycles in T^d x SU(2). DynamIC Preprint 2016-10
  • Nikolaos Karaliolios, Differentiable Rigidity for quasiperiodic cocycles in compact Lie groups. DynamIC Preprint 2016-9
  • Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle. DynamIC Preprint 2016-6
  • Peter Giesl, Boumediene Hamzi, Martin Rasmussen, and Kevin N. Webster, Approximation of Lyapunov functions from noisy data. DynamIC Preprint 2016-1
  • Alexander M. Henderson, Eric J. Olson, James C. Robinson, and Nicholas Sharples, Equi-homogeneity, Assouad dimension and non-autonomous dynamics. DynamIC Preprint 2014-7
2017
  • Anna Maria Cherubini, Jeroen S. W. Lamb, Martin Rasmussen, and Yuzuru Sato, A random dynamical systems perspective on stochastic resonance, Nonlinearity 30, 7 (2017), 2835−2853. Article MathSciNet Preprint
  • 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
2016
  • Martin Rasmussen, Alan Hastings, Matthew J. Smith, Folashade B. Agusto, Benito M. Chen-Charpentier, Forrest M. Hoffman, Jiang Jiang, Katherine E. O. Todd-Brown, Ying Wang, Ying-Ping Wang, and Yiqi Luo, Transit times and mean ages for nonautonomous and autonomous compartmental systems, Journal of Mathematical Biology 73, 6−7 (2016), 1379−1398. Article MathSciNet Preprint
2015
  • Vasso Anagnostopoulou, Tobias Jäger, and Gerhard Keller, A model for the nonautonomous Hopf bifurcation, Nonlinearity 28, 7 (2015), 2587−2616. MathSciNet Preprint
  • Thai Son Doan, Anke Kalauch, Markus Klose, and Stefan Siegmund, Stability of positive linear switched systems on ordered Banach spaces, Systems & Control Letters 75(2015), 14−19. 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
2014
  • 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
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
  • 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
  • Weixiao Shen and Sebastian van Strien, On stochastic stability of expanding circle maps with neutral fixed points, Dynamical Systems 28, 3 (2013), 423−452. 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
  • Peter Giesl and Martin Rasmussen, Areas of attraction for nonautonomous differential equations on finite time intervals, Journal of Mathematical Analysis and Applications 390, 1 (2012), 27−46. Article MathSciNet
2011
  • Stefan Liebscher, Jörg Härterich, Kevin N. Webster, and Marc Georgi, Ancient dynamics in Bianchi models: approach to periodic cycles, Communications in Mathematical Physics 305, 1 (2011), 59−83. Article MathSciNet
  • Oleg Makarenkov and Rafael Ortega, Asymptotic stability of forced oscillations emanating from a limit cycle, Journal of Differential Equations 250, 1 (2011), 39−52. Article MathSciNet
2010
  • 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
  • Adriana Buică, Jaume Llibre, and Oleg Makarenkov, Asymptotic stability of periodic solutions for nonsmooth differential equations with application to the nonsmooth van der Pol oscillator, SIAM Journal on Mathematical Analysis 40, 6 (2009), 2478−2495. Article 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
  • Martin Rasmussen, All-time Morse decompositions of linear nonautonomous dynamical systems, Proceedings of the American Mathematical Society 136, 3 (2008), 1045−1055. 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
  • Oleg Kozlovski, Weixiao Shen, and Sebastian van Strien, Density of hyperbolicity in dimension one, Annals of Mathematics 166, 1 (2007), 145−182. Article MathSciNet
  • Martin Rasmussen, Attractivity and bifurcation for nonautonomous dynamical systems, Lecture Notes in Mathematics 1907, Springer, Berlin, 2007. MathSciNet
  • Martin Rasmussen, Morse decompositions of nonautonomous dynamical systems, Transactions of the American Mathematical Society 359, 10 (2007), 5091−5115. Article MathSciNet
2006
  • Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Invariant manifolds as pullback attractors of nonautonomous differential equations, Discrete and Continuous Dynamical Systems A 15, 2 (2006), 579−596. Article MathSciNet
2005
  • Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Approximation of attractors of nonautonomous dynamical systems, Discrete and Continuous Dynamical Systems B 5, 2 (2005), 215−238. Article MathSciNet
  • Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Invariant manifolds as pullback attractors of nonautonomous difference equations, in: Proceedings of the Eighth International Conference on Difference Equations and Applications (S. Elaydi, G. Ladas, B. Aulbach, O. Dosly), 23−37, CRC, Boca Raton, 2005. 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
  • Stefano Luzzatto, Ian Melbourne, and Frederic Paccaut, The Lorenz attractor is mixing, Communications in Mathematical Physics 260, 2 (2005), 393−401. Article MathSciNet
2004
  • 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
2001
  • 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
1999
  • 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
1998
  • Jeroen S. W. Lamb and Matthew Nicol, On symmetric attractors in reversible dynamical systems, Physica D 112, 1−2 (1998), 281−297. 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
  • 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, and Dmitry Turaev, Quasiattractors and homoclinic tangencies, Computers & Mathematics with Applications 34, 2−4 (1997), 195−227. Article 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
  • Jeroen S. W. Lamb and Matthew Nicol, On symmetric omega-limit sets in reversible flows, in: Nonlinear Dynamical Systems and Chaos, Progress in Nonlinear Differential Equations and Their Applications, 103−120, Birkhäuser, Basel, 1996. MathSciNet
1993
  • 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
1989
  • Jean-Marc Gambaudo, Sebastian van Strien, and Charles Tresser, Hénon-like maps with strange attractors: there exist C^\infty Kupka-Smale diffeomorphisms on S^2 with neither sinks nor sources, Nonlinearity 2, 2 (1989), 287−304. 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