Fermi acceleration / Arnold diffusion / Adiabatic invariants

A.Neishtadt, A.Artemyev, D.Turaev, Remarkable charged particle dynamics near magnetic field null lines, Chaos 29, 051104 (2019)

C.Dettmann, V.Fain, D.Turaev, Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse, Nonlinearity 31, 667-700 (2018)

V.Gelfreich, D.Turaev, Arnold Diffusion in a priori chaotic symplectic maps, Comm. Math. Phys. 353, 507-547 (2017)

K.Shah, D.Turaev, V.Gelfreich, V.Rom-Kedar, Equilibration of energy in slow-fast systems, PNAS (2017)

D.Turaev, Averaging over a non-ergodic subsystem, "Anosov Systems and Modern Dynamics" abstracts book(2016)

D.Turaev, Exponential energy growth due to slow parameter oscillations in quantum mechanical systems, Phys. Rev. E 93, 050203(R) (2016)

K.Shah, V.Gelfreich, V.Rom-Kedar, D.Turaev, Leaky Fermi accelerators, Phys. Rev. E91, 062920 (2015)

T.Pereira, D.Turaev, Fast Fermi acceleration and entropy growth , Math. Model. Nat. Phenom. 10, 31-47 (2015)

T.Pereira, D.Turaev, Exponential energy growth in adiabatically changing Hamiltonian systems, Phys. Rev. E91, 010901(R) (2015)

V.Gelfreich, V.Rom-Kedar, D.Turaev, Oscillating mushrooms: adiabatic theory for a non-ergodic system, J. Phys. A 47, 395101 (2014)

D.Turaev, Exponential Fermi acceleration in adiabatically perturbed Hamiltonian systems, Proceedings of the 8th European Nonlinear Dynamics Conference (ENOC 2014)

D.Turaev, C.Warner, S.Zelik, Energy growth for a nonlinear oscillator coupled to a monochromatic wave, Regul. Chaotic Dyn. 19, 513-522 (2014)

V.Gelfreich, V.Rom-Kedar, D.Turaev, Fermi acceleration and adiabatic invariants for non-autonomous billiards, Chaos 22, 033116 (2012)

D.Turaev, On the splitting of invariant curves, Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011)

V.Gelfreich, V.Rom-Kedar, K.Shah, D.Turaev, Robust exponential acceleration in time-dependent billiards, Phys. Rev. Lett. 106, 074101 (2011)

K.Shah, D.Turaev, V.Rom-Kedar, Exponential energy growth in a Fermi accelerator, Phys. Rev. E 81, 056205 (2010)

V.Gelfreich, D.Turaev, Fermi acceleration in non-autonomous billiards, J. Phys. A 41, 212003 (2008)

V.Gelfreich, D.Turaev, Unbounded energy growth in Hamiltonian systems with slowly varying parameter, Commun. Math. Phys. 283, 769-794 (2008)

V.Rom-Kedar , D.Turaev, The symmetric parabolic resonance, Nonlinearity 23, 1325-1351 (2010)

      Billiard-like potentials

D.Turaev, C.Warner, S.Zelik, Energy growth for a nonlinear oscillator coupled to a monochromatic wave, Regul. Chaotic Dyn. 19, 513-522 (2014)

V.Rom-Kedar, D.Turaev, Billiards: A singular perturbation limit of smooth Hamiltonian flows, Chaos 22, 026102 (2012)

A.Rapoport, V.Rom-Kedar, D.Turaev, Stability in high-dimensional steep repelling potentials, Commun. Math. Phys. 279 (2008)

A.Rapoport, V.Rom-Kedar, D.Turaev, Approximating multi-dimensional Hamiltonian flows by billiards, Commun. Math. Phys. 272, 567-600 (2007)

D.Turaev, V.Rom-Kedar, Soft billiards with corners, J. Stat. Phys. 112, 765-813 (2003)

V.Rom-Kedar, D.Turaev, Big islands in dispersing billiard-like potentials, Physica D130, 187-210 (1999)

D.Turaev, V.Rom-Kedar, Elliptic islands appearing in near-ergodic flows, Nonlinearity 11, 575-599 (1998)

D.Turaev, V.Rom-Kedar, On smooth Hamiltonian flows limiting to ergodic billiards, in "Chaos, kinetics and nonlinear dynamics in liquids and plasmas," Lect. Notes in Physics (1998)

      Homoclinic loops / Superhomoclinic loops / Solitons

D.Turaev, Hyperbolic sets near homoclinic loops to a saddle for systems with a first integral, Regul. Chaotic Dyn. 19, 681-693 (2014)

W.Giles, J.S.W.Lamb, D.Turaev, On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems, Nonlinearity 29, 3148-3173 (2016)

D.Turaev, Multi-pulse homoclinic loops in systems with a smooth first integral, in "Ergodic theory, analysis, and efficient simulation of dynamical systems" (Springer-Verlag, 2001)

L.P.Shilnikov, D.Turaev, Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries, Regul. Chaotic Dyn. 2, 126-138 (1997)

D.Turaev, L.P.Shilnikov, On Hamiltonian systems with homoclinic saddle curves, Sov. Math. Dokl. 39, 165-168 (1989)

D.Turaev, L.P.Shilnikov, On Hamiltonian systems with homoclinic curves of a saddle, in "Nonlinear and turbulent processes in physics," 148-151 (Naukova Dumka, 1988)

V.M.Eleonsky, N.E.Kulagin, D.Turaev, L.P.Shilnikov, Classification of self-localized states of an electromagnetic field in a nonlinear medium, Soviet Phys. Doklady 34 (1989)

V.M.Eleonsky, N.E.Kulagin, D.Turaev, L.P.Shilnikov, On the classification of self-localized states of the electromagnetic field within nonlinear medium, Methods of qualitative theory and theory of bifurcations, 32-45 (1988)

D.Turaev, M.Radziunas, A.Vladimirov, Chaotic soliton walk in periodically modulated media, Phys. Rev. E 77(R) (2008)

      Homoclinic tangency / Elliptic points / Richness of chaos

P.Berger, D.Turaev, On Herman's positive entropy conjecture, Advances in Mathematics 349, 1234-1288 (2019)

S.V.Gonchenko, D.Turaev, L.Shilnikov, Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps, Nonlinearity 20, 241-275 (2007)

S.V.Gonchenko, D.Turaev, L.Shilnikov, Homoclinic tangencies of arbitrarily high orders in conservative two-dimensional maps, Doclady Math. 73, 210-213 (2006)

V.Gelfreich, D.Turaev, Universal dynamics in a neighbourhood of a generic elliptic periodic point, Regul. Chaotic Dyn. 15,159-164 (2010)

D.Turaev, Polynomial approximations of symplectic dynamics and richness of chaos in nonhyperbolic area-preserving maps, Nonlinearity 16, 1-13 (2003)

S.V.Gonchenko, D.V.Turaev, L.P.Shilnikov, Infinitely many elliptic periodic orbits in four-dimensional symplectic diffeomorphisms with a homoclinic tangency, Proc. Steklov Inst. Math. 244, 106-131 (2004)

S.V.Gonchenko, L.P.Shilnikov, D.Turaev, Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom, Regul. Chaotic Dyn. 3, 3-26 (1998)