English

Almost equivalence of suspension Anosov flows

Dynamical Systems 2026-03-23 v2 Geometric Topology

Abstract

We provide a written proof of a result due to H. Minakawa, which states that all suspension Anosov flows generated by hyperbolic matrices with positive trace are pairwise almost equivalent. The proof relies on constructing, for any given suspension flow, a genus-one Birkhoff section whose first-return map has fewer fixed points than the original map. We improve Minakawa's result by explicitly calculating the first return map onto this section, which leads to explicit bounds on the distances between suspension Anosov flows within the graph of Anosov flows.

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Cite

@article{arxiv.1910.08457,
  title  = {Almost equivalence of suspension Anosov flows},
  author = {Mario Shannon and Pierre Dehornoy},
  journal= {arXiv preprint arXiv:1910.08457},
  year   = {2026}
}