Liouville ergodicity of linear multi-particle hamiltonian system with one marked particle velocity flips
Mathematical Physics
2016-11-02 v1 Dynamical Systems
math.MP
Abstract
We consider multi-particle systems with linear deterministic hamiltonian dynamics. Besides Liouville measure it has continuum of invariant tori and thus continuum of invariant measures. But if one specified particle is subjected to a simple linear deterministic transformation (velocity flip) in random time moments, we prove convergence to Liouville measure for any initial state. For the proof it appeared necessary to study non-linear transformations on the energy surface.
Keywords
Cite
@article{arxiv.1503.04531,
title = {Liouville ergodicity of linear multi-particle hamiltonian system with one marked particle velocity flips},
author = {A. A. Lykov and V. A. Malyshev},
journal= {arXiv preprint arXiv:1503.04531},
year = {2016}
}