On the relation between action and linking

David Bechara Senior; Umberto L. Hryniewicz; Pedro A. S. Salomão

doi:10.3934/jmd.2021011

Article Contents

2021, Volume 17: 319-336. Doi: 10.3934/jmd.2021011

This volume Previous Article Non-autonomous curves on surfaces Next Article Horospherically invariant measures and finitely generated Kleinian groups

On the relation between action and linking

1.
Ruhr-Universität Bochum, Universitätsstrasse 150, IB 3/79, Bochum 44801, Germany
2.
RWTH Aachen, Jakobstrasse 2, Aachen 52064, Germany
3.
Instituto de Matemática e Estatística, Departamento de Matemática, Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, São Paulo, SP 05508-090, Brazil and NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China

Received: July 31, 2020

Revised: April 09, 2021

Published: July 2021

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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.

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Mathematics Subject Classification: Primary: 37D05; Secondary: 53D10.

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References

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