Time-dependent billiards, variational method, and invariant tori

DOI10.1088/1361-6544/AD953BMaRDI QIDQ6668489

Xianbin Liu, Xiao-Ming Zhang, Denghui Li

Publication date: 22 January 2025

Published in: Nonlinearity (Search for Journal in Brave)

zbMATH Keywords

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Mathematics Subject Classification ID

Dynamics of a system of particles, including celestial mechanics (70F99) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Other variational principles in mechanics (70H30)

Cites Work

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• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
• On the periodic motions of dynamical systems.
• KAM theory in configuration space
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Stability analysis of the breathing circle billiard
• Symplectic twist maps. Global variational techniques
• A Lagrangian proof of the invariant curve theorem for twist mappings
• Instability in Fermi-Ulam `ping-pong' problem
• Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse
• Bounded gain of energy on the breathing circle billiard

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