English

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 CC can be split into a Reeb dynamics on an open subset of CC and a Liouville dynamics on a submanifold of CC 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