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arXiv · 2602.15719

Weak mixing for area preserving flows on surfaces

Adam Kanigowski·Alexey Okunev·Rigoberto Zelada
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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.

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Adam Kanigowski, Alexey Okunev, Rigoberto Zelada. 2026-02-17. Weak mixing for area preserving flows on surfaces. https://arxiv.org/abs/2602.15719

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