Chaotic Boltzmann billiard systems at positive energy

Abstract

This paper deals with the 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 real 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 for $\beta$ sufficiently small.