Construction and upper bound on the minimum genus of an embedded surface with Anosov geodesic flow

Victor Donnay; Daniel Visscher

Construction and upper bound on the minimum genus of an embedded surface with Anosov geodesic flow

Dynamical Systems 2026-07-09 v1

Authors: Victor Donnay , Daniel Visscher

Abstract

We create examples of smooth, compact surfaces in $R^3$ for which the geodesic flow is Anosov. We determine their genus, thereby giving a (non-sharp) upper bound for the minimal genus of an embedded surface with Anosov geodesic flow. These examples are explicit physically realizable Anosov systems.

Keywords

Anosov geodesic flow embedded surface minimum genus smooth compact surface

Cite

@article{arxiv.2607.08439,
  title  = {Construction and upper bound on the minimum genus of an embedded surface with Anosov geodesic flow},
  author = {Victor Donnay and Daniel Visscher},
  journal= {arXiv preprint arXiv:2607.08439},
  year   = {2026}
}