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Legendrian persistence modules and dynamics

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Abstract

We relate the machinery of persistence modules to the Legendrian contact homology theory and to Poisson bracket invariants, and use it to show the existence of connecting trajectories of contact and symplectic Hamiltonian flows.

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Acknowledgements

We thank F. Bourgeois, B. Chantraine, G. Dimitroglou Rizell, T. Ekholm, Y. Eliashberg, E. Giroux, and M. Sullivan for useful discussions. We also thank A. Fathi for communicating to us his unpublished note [32] containing Theorem 2.1 and its proof. We thank T. Melistas, J. Zhang, and the anonymous referee for numerous corrections, and G. Dimitroglou Rizell for finding a mistake in the original version of Theorem 1.5(ii).

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Authors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel, 32000

    Michael Entov

  2. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel, 69978

    Leonid Polterovich

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  1. Michael Entov
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  2. Leonid Polterovich
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Correspondence to Leonid Polterovich.

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To Claude Viterbo on the occasion of his 60th birthday.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

In this article the affiliation details for Author Leonid Polterovich were incorrectly given as Technion-Israel Institute of Technology, Haifa, and Tel Aviv University, but should have been Tel Aviv University. The article has been corrected.

Michael Entov was partially supported by the Israel Science Foundation grant 1715/18. Leonid Polterovich was partially supported by the Israel Science Foundation grant 1102/20.

This article is part of the topical collection “Symplectic geometry—A Festschrift in honour of Claude Viterbo’s 60th birthday” edited by Helmut Hofer, Alberto Abbondandolo, Urs Frauenfelder, and Felix Schlenk.

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Entov, M., Polterovich, L. Legendrian persistence modules and dynamics. J. Fixed Point Theory Appl. 24, 30 (2022). https://doi.org/10.1007/s11784-022-00944-x

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