A mechanical counterexample to KAM theory with low regularity

DOI10.1016/j.physd.2014.05.010zbMath1349.70037arXiv2004.09940OpenAlexW2004927227WikidataQ124823526 ScholiaQ124823526MaRDI QIDQ2832923

Stefano Marò

Publication date: 15 November 2016

Published in: Physica D: Nonlinear Phenomena (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.09940

zbMATH Keywords

KAM theorybouncing ballunbounded orbits

Mathematics Subject Classification ID

Collision of rigid or pseudo-rigid bodies (70F35) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (5)

On unbounded motions in a real analytic bouncing ball problem ⋮ Diffusion and chaos in a bouncing ball model ⋮ Some remarks on the periodic motions of a bouncing ball ⋮ A \(C^{1+\alpha}\) mechanical counterexample to Moser's twist theorem ⋮ Chaotic motion in the breathing circle billiard

Cites Work

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• Complete orbits for twist maps on the plane: extensions and applications
• Bouncing balls in nonlinear potentials
• Total destruction of Lagrangian tori
• Invariant Curves of Mappings with Averaged Small Twist
• Stable and Random Motions in Dynamical Systems
• The dynamics of repeated impacts with a sinusoidally vibrating table
• Instability in Fermi-Ulam `ping-pong' problem
• Coexistence of bounded and unbounded motions in a bouncing ball model
• Periodic Motions of Linear Impact Oscillators via the Successor Map

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