Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 21 Oct 2020Embargo end date: 01 Jan 2020 Spain, Italy Publisher:IOP PublishingJournal:Journal of Physics A: Mathematical and Theoretical, volume 53, page 455,205 (issn: 1751-8113, eissn: 1751-8121,

Copyright policy )

Authors: A Bravetti; M de León; J C Marrero; E Padrón;

doi: 10.1088/1751-8121/abbaaa , 10.48550/arxiv.2006.15123

arXiv: 2006.15123

handle: 10261/233267 , 11581/484793

Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread

- Summary
- Subjects
- Metrics

Abstract

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.

Countries

Spain, Italy

Related Organizations

Spanish National Research Council
Spain
National Autonomous University of Mexico
Mexico
University of La Laguna
Spain
University of Camerino
Italy

Keywords

Contact systems, Mathematics - Differential Geometry, Reeb dynamics, invariant measure, FOS: Physical sciences, Mathematical Physics (math-ph), 37A05, 37J55, 53D10, 70G45, 70H05, Differential Geometry (math.DG), Mathematics - Symplectic Geometry, FOS: Mathematics, Contact manifolds (general theory), exact symplectic manifold, Symplectic Geometry (math.SG), Liouville vector field, contact Hamiltonian system, Mathematical Physics

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	32
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%