Lyapunov 1-forms on orbifolds
Differential Geometry
2025-12-02 v1 Algebraic Topology
Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2512.01879,
title = {Lyapunov 1-forms on orbifolds},
author = {Fabricio Valencia},
journal= {arXiv preprint arXiv:2512.01879},
year = {2025}
}
Comments
18 pages. Preliminary version. Comments are very welcome