Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
Mathematical Physics
2020-12-02 v2 Differential Geometry
math.MP
Symplectic Geometry
Abstract
We prove that, under some natural conditions, Hamiltonian systems on a contact manifold can be split into a Reeb dynamics on an open subset of and a Liouville dynamics on a submanifold of of codimension 1. For the Reeb dynamics we find an invariant measure. Moreover, we show that, under certain completeness conditions, the existence of an invariant measure for the Liouville dynamics can be characterized using the notion of a symplectic sandwich with contact bread.
Keywords
Cite
@article{arxiv.2006.15123,
title = {Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread},
author = {Alessandro Bravetti and Manuel de León and Juan Carlos Marrero and Edith Padrón},
journal= {arXiv preprint arXiv:2006.15123},
year = {2020}
}
Comments
21 pages, no figures, it matches the final version accepted in JPA