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arXiv · 2509.17132

Chaotic Boltzmann's Billiard Systems at positive energy

Irene De Blasi·Airi Takeuchi·Susanna Terracini
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Abstract

This paper deals with the so-called Boltzmann billiard, that is, a billiard subjected to a central force of the type $V(r)=-\alpha/r-\beta/r^2$, $\alpha$ and $\beta$ being positive constants, and with a straight reflection table. In the particular case of $\alpha$ and $\beta$ positive, we prove the presence of a symbolic dynamics, and hence of positive topological entropy, at positive energy and for $\beta$ sufficiently small.

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Irene De Blasi, Airi Takeuchi, Susanna Terracini. 2025-09-21. Chaotic Boltzmann's Billiard Systems at positive energy. https://arxiv.org/abs/2509.17132

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