Lyapunov 1-forms on orbifolds

TL;DR

This paper introduces a new concept of smooth Lyapunov 1-forms for flows on orbifolds, providing topological conditions for their existence based on asymptotic cycles and chain-recurrent sets.

Contribution

It extends the theory of Lyapunov 1-forms to orbifolds and establishes conditions for their existence in a cohomology class, advancing the understanding of dynamical systems on orbifolds.

Findings

Topological conditions for Lyapunov 1-form existence on orbifolds

Use of asymptotic cycles and chain-recurrent sets in analysis

Extension of Lyapunov theory to orbifold settings

Abstract

We introduce and analyze a notion of smooth Lyapunov 1-form for flows generated by vector fields on orbifolds. Using asymptotic cycles and chain-recurrent sets, we establish topological conditions that guarantee the existence of a Lyapunov 1-form, lying in a prescribed cohomology class, for a given vector field on a compact orbifold.