Existence of periodic solutions in the systems of the billiard type

DOI10.1007/S12346-021-00514-5zbMath1482.34112OpenAlexW3194469949MaRDI QIDQ1981912

Zhenbang Cao, Denghui Li, Jian-Hua Xie, Xiao-Ming Zhang

Publication date: 7 September 2021

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-021-00514-5

zbMATH Keywords

approximation schemebilliard like systemdissipation systemperiodic bounce solution

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Theoretical approximation of solutions to ordinary differential equations (34A45)

Related Items (1)

Stability analysis of the breathing circle billiard

Cites Work

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• Periodic solutions of dissipative systems revisited
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• \(L^{\infty}\) bounds for solutions of parametrized elliptic equations
• Periodic bounce trajectories with a low number of bounce points
• On the approximation of the elastic bounce problem on Riemannian manifolds
• Stability theory and the existence of periodic solutions and almost periodic solutions
• Diffusion and chaos in a bouncing ball model
• Existence of invariant curves for a Fermi-type impact absorber
• Normal modes of a Lagrangian system constrained in a potential well
• Chaotic dynamics in an impact problem
• Approximating multi-dimensional Hamiltonian flows by billiards
• Billiards: A singular perturbation limit of smooth Hamiltonian flows
• Periodic Bounce Orbits of Prescribed Energy

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