Pinball dynamics: unlimited energy growth in switching Hamiltonian systems

DOI10.1007/s00220-015-2386-9zbMath1343.37049arXiv1303.5510OpenAlexW1560884718MaRDI QIDQ2351052

Maxim Arnold, Vadim Zharnitsky

Publication date: 26 June 2015

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5510

Mathematics Subject Classification ID

Growth and boundedness of solutions to ordinary differential equations (34C11) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Discontinuous ordinary differential equations (34A36) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

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Cites Work

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• Invariant curves and time-dependent potentials
• Instability in Fermi-Ulam `ping-pong' problem
• On products of skew rotations
• Hyperbolic outer billiards: a first example
• On a conjecture of Erdös and Szüsz related to uniform distribution mod 1

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