Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse

DOI10.1088/1361-6544/aa9ee5zbMath1388.37067arXiv1706.08623OpenAlexW2963001435MaRDI QIDQ4635049

Vitaly Fain, Dmitry V. Turaev, Carl P. Dettmann

Publication date: 13 April 2018

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.08623

zbMATH Keywords

Arnold diffusionHamiltonian systemseparatrix splittingscattering mapFermi accelerationenergy growthelliptic billiard

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Systems with slow and fast motions for nonlinear problems in mechanics (70K70)

Related Items (5)

Critical Velocity for the Onset of Fast Fermi Acceleration ⋮ Stability analysis of the breathing circle billiard ⋮ Arnold diffusion in multidimensional convex billiards ⋮ Degenerate Chenciner Bifurcation Revisited ⋮ Chaotic motion in the breathing circle billiard

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