English

Skewed Anosov flows are orbit equivalent to Reeb-Anosov flows in dimension 3

Dynamical Systems 2025-10-30 v4 Symplectic Geometry

Abstract

We prove that in dimension 3, Anosov flows which are R\mathbb{R}-covered and skewed are orbit equivalent to Reeb-Anosov flows. We characterize the existence of an invariant contact form or of a Birkhoff section with a given boundary, in terms of linking numbers between two invariant signed measures. Furthermore, we prove the existence of open book decompositions with one boundary component for Reeb-Anosov flows.

Keywords

Cite

@article{arxiv.2301.00842,
  title  = {Skewed Anosov flows are orbit equivalent to Reeb-Anosov flows in dimension 3},
  author = {Théo Marty},
  journal= {arXiv preprint arXiv:2301.00842},
  year   = {2025}
}

Comments

73 pages, 3 appendices, 8 figures, 1 table. New version: Section 1 and 2 were merged, explanation were added in section 5, many mistakes were corrected, two figures were added