Partial section I: $\alpha$-recurrence and equivariant Lyapunov maps

Théo Marty

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arXiv · 2512.04994

Partial section I: $\alpha$-recurrence and equivariant Lyapunov maps

Théo Marty

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Abstract

This is the first article in a series that aims at classifying partial sections of flows, that is a general family of transverse surfaces. In this part, we deal with the dynamical aspect of the question. Given a flow on a compact manifold $M$ and a cohomology class $\alpha$ of rank 1, we give a criterion for the existence of an $\alpha$-equivariant Lyapunov map on an Abelian covering of $M$ associated to $\alpha$. One important aspect of the existence of such Lyapunov maps, and of the classification of partial sections, is a type of recurrence set relative to $\alpha$. We describe how that set depends on $\alpha$.

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Théo Marty. 2025-12-04. Partial section I: $\alpha$-recurrence and equivariant Lyapunov maps. https://arxiv.org/abs/2512.04994

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