Weak mixing for area preserving flows on surfaces

Adam Kanigowski; Alexey Okunev; Rigoberto Zelada

Weak mixing for area preserving flows on surfaces

Dynamical Systems 2026-02-18 v1

Authors: Adam Kanigowski , Alexey Okunev , Rigoberto Zelada

Abstract

Let $(\phi_t)$ be an area-preserving smooth flow on a compact, connected, orientable surface $\mathcal M$ with at least one but finitely many fixed points. Assume that $(\phi_t)$ is analytic (up to a canonical change of coordinates) in the neighborhood of each saddle fixed point. We show that the flow $(\phi_t)$ is weakly mixing on each of its (finitely many) quasi-minimal components.

Keywords

geodesic flow weak convergence minimal surfaces

Cite

@article{arxiv.2602.15719,
  title  = {Weak mixing for area preserving flows on surfaces},
  author = {Adam Kanigowski and Alexey Okunev and Rigoberto Zelada},
  journal= {arXiv preprint arXiv:2602.15719},
  year   = {2026}
}

Comments

36 pages, 2 figures

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