The \(K\)-property of Hamiltonian systems with restricted hard ball interactions
This paper examines a variant of the Chernov-Sinai pencase model for the study of a mechanical system of elastic hard balls. In the Chernov-Sinai model, large hard ball particles move on a torus which is elongated in one spatial dimension. The cyclic order of the particles remains invariant, so each ball can interact only with its two neighbors. Chernov and Sinai used this model because the restricted form of the interactions was expected to make ergodicity easier to establish, and because this quasi-one-dimensional mechanical model seems to be suitable for studying the hydrodynamic limit transition. The authors of this paper treat a similar case where the balls have a graph of interactions which is a tree or a circle of length \(N\). They prove that the standard billiard ball systems with interactions so restricted is a \(K\)-flow.
billiard system with restricted interactions
scientific article; zbMATH DE number 858522