English

On the relation between action and linking

Symplectic Geometry 2021-04-28 v4 Dynamical Systems

Abstract

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.

Keywords

Cite

@article{arxiv.2006.06266,
  title  = {On the relation between action and linking},
  author = {David Bechara Senior and Umberto L. Hryniewicz and Pedro A. S. Salomão},
  journal= {arXiv preprint arXiv:2006.06266},
  year   = {2021}
}

Comments

16 pages; v4 incorporates corrections and suggestions from all referee reports

R2 v1 2026-06-23T16:13:46.666Z