Projective Dynamics and an Integrable Boltzmann Billiard Model

2020/10/28 by Lei Zhao, Zhao, Lei · 2 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Quantum chaos and dynamical systems #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2010.15257

Abstract

The aim of this note is to explain the integrability of an integrable Boltzmann billiard model, previously established by Gallavotti and Jauslin in arXiv:2008.01955, alternatively via the viewpoint of projective dynamics. The additional first integral is shown to be related to the energy of a corresponding system on a hemisphere. We show that this viewpoint applies to certain other billiard models in the plane defined through Kepler-Coulomb problems as well. The approach also leads to a family of integrable billiard models on the sphere defined through the spherical Kepler-Coulomb problem.

Cited by

• Projective deduction of the non-trivial first integral to the Euler problem: an explicit computation
• Chaotic Boltzmann's Billiard Systems at positive energy
• Non-integrability of n-centre billiards

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