Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread Articles uri icon

authors

  • Bravetti, A.
  • LEON RODRIGUEZ, MANUEL DE
  • Marrero, J. C.
  • Padron, E.

publication date

  • October 2020

start page

  • 1

end page

  • 25

issue

  • 45

volume

  • 53

International Standard Serial Number (ISSN)

  • 1751-8113

Electronic International Standard Serial Number (EISSN)

  • 1751-8121

abstract

  • We prove that, under some natural conditions, Hamiltonian systems on a contact manifold C can be split into a Reeb dynamics on an open subset of C and a Liouville dynamics on a submanifold of C 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

  • contact hamiltonian system; reeb dynamics; exact symplectic manifold; liouville vector field; invariant measure