PreprintCC BY-NC 4.0HAL
Almost equivalence of suspension Anosov flows
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.
Related
- Finiteness of Anosov and pseudo-Anosov flows on hyperbolic 3-manifolds
- Klingenberg's theorem on Anosov geodesic flows
- Construction of Anosov flows on fibered hyperbolic 3-manifolds
- Exotic codimension one Anosov flows
- Rigidity from the strong unstable foliation for higher-dimensional Anosov and partially hyperbolic flows
BibTeX
@misc{dehornoy2026almost,
title = {{Almost equivalence of suspension Anosov flows}},
author = {Pierre Dehornoy and Mario Shannon},
howpublished = {HAL},
year = {2026},
month = jul,
eprint = {1910.08457},
archivePrefix = {arXiv},
url = {https://hal.science/hal-02317541v3},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Almost equivalence of suspension Anosov flows
AU - Pierre Dehornoy
AU - Mario Shannon
PY - 2026
DA - 2026/07/18
PB - HAL
UR - https://hal.science/hal-02317541v3
AB - 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.
ER -