Publications – Dynamical Systems at Imperial College London (DynamIC)

Andrew Clarke, Generic Properties of Geodesic Flows on Convex Hypersurfaces of Euclidean Space. DynamIC Preprint 2019-9
Andrew Clarke and Dmitry Turaev, Arnold diffusion in multi-dimensional convex billiards. DynamIC Preprint 2019-8

2022

Sajjad Bakrani, Jeroen S. W. Lamb, and Dmitry Turaev, Invariant manifolds of homoclinic orbits and the dynamical consequences of a super-homoclinic: a case study in $\Bbb R^4$ with $\Bbb Z_2$-symmetry and integral of motion, Journal of Differential Equations 327(2022), 1−63. Article MathSciNet

2020

Alessandro Duca, Romain Joly, and Dmitry Turaev, Permuting quantum eigenmodes by a quasi-adiabatic motion of a potential wall, Journal of Mathematical Physics 61, 10 (2020), 101511, 15. Article MathSciNet
Jeroen S. W. Lamb, Mauricio F. S. Lima, Ricardo M. Martins, Marco Antonio Teixeira, and Jiazhong Yang, On the Hamiltonian structure of normal forms at elliptic equilibria of reversible vector fields in $\BbbR^4$, Journal of Differential Equations 269, 12 (2020), 11366−11395. Article MathSciNet Preprint

2018

Carl P. Dettmann, Vitaly Fain, and Dmitry Turaev, Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse, Nonlinearity 31, 3 (2018), 667−700. Article MathSciNet

2017

Vassili Gelfreich and Dmitry Turaev, Arnold diffusion in a priori chaotic symplectic maps, Communications in Mathematical Physics 353, 2 (2017), 507−547. Article MathSciNet
Kushal Shah, Dmitry Turaev, Vassili Gelfreich, and Vered Rom-Kedar, Equilibration of energy in slow-fast systems, Proceedings of the National Academy of Sciences of the United States of America 114, 49 (2017), E10514−E10523. Article MathSciNet

2016

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 Preprint

2015

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

2014

Vassili Gelfreich, Vered Rom-Kedar, and Dmitry Turaev, Oscillating mushrooms: adiabatic theory for a non-ergodic system, Journal of Physics A 47, 39 (2014), 395101, 21. MathSciNet
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

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
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

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
Georg Ostrovski and Sebastian van Strien, Piecewise linear Hamiltonian flows associated to zero-sum games: transition combinatorics and questions on ergodicity, Regular and Chaotic Dynamics 16, 1−2 (2011), 128−153. Article MathSciNet
Sebastian van Strien, Hamiltonian flows with random-walk behaviour originating from zero-sum games and fictitious play, Nonlinearity 24, 6 (2011), 1715−1742. 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

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
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

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
Martijn van Noort, Mason A. Porter, Yingfei Yi, and Shui-Nee Chow, Quasiperiodic dynamics in Bose-Einstein condensates in periodic lattices and superlattices, Journal of Nonlinear Science 17, 1 (2007), 59−83. 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
Bob Rink, Proof of Nishida's conjecture on anharmonic lattices, Communications in Mathematical Physics 261, 3 (2006), 613−627. Article MathSciNet
R. Mark Roberts, Tanya Schmah, and Cristina Stoica, Relative equilibria in systems with configuration space isotropy, Journal of Geometry and Physics 56, 5 (2006), 762−779. 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

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

2003

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
Dmitry Turaev and Vered Rom-Kedar, Soft billiards with corners, Journal of Statistical Physics 112, 3−4 (2003), 765−813. Article MathSciNet

2002

R. Mark Roberts, Claudia Wulff, and Jeroen S. W. Lamb, Hamiltonian systems near relative equilibria, Journal of Differential Equations 179, 2 (2002), 562−604. 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

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

1997

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

1996

Jeroen S. W. Lamb, Area-preserving dynamics that is not reversible, Physica A 228, 1−4 (1996), 344−365. 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

Jeroen S. W. Lamb, Crystallographic symmetries of stochastic webs, Journal of Physics A 26(1993), 2921−2933.

1992

Jeroen S. W. Lamb, The ferro-antiferro bifurcation transition in a microscopic model with incommensurate phases, Journal of Physics A 25(1992), 355−365.

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