2020/06/11 by David Bechara Senior, Senior, David Bechara, Umberto L. Hryniewicz +3 · 2 citations
Mathematics · #37J06 #53Dxx #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DS #math.SG #msc:37J06 #msc:53Dxx
paper · pdf · doi:10.48550/arxiv.2006.06266
16 pages; v4 incorporates corrections and suggestions from all referee reports
arxiv created 2021/04/27 · arxiv updated 2021/04/28
We introduce numerical invariants of contact forms in dimension three and use asymptotic cycles to estimate them. As a consequence, we prove a version for Anosov Reeb flows of results due to Hutchings and Weiler on mean actions of periodic points. The main tool is the Action-Linking Lemma, expressing the contact area of a surface bounded by periodic orbits as the Liouville average of the asymptotic intersection number of most trajectories with the surface.