The Lyapunov Exponents of Hyperbolic Measures for $C^1$ Vector Fields with Dominated Splitting
Dynamical Systems
2026-01-01 v1
Abstract
In this paper, we prove that for every vector field preserving an ergodic hyperbolic invariant measure which is not supported on singularities, if the Oseledec splitting of the ergodic hyperbolic invariant measure is a dominated splitting, then the ergodic hyperbolic invariant measure can be approximated by periodic measures, and the Lyapunov exponents of the ergodic hyperbolic invariant measure can also be approximated by the Lyapunov exponents of those periodic measures.
Keywords
Cite
@article{arxiv.2512.24911,
title = {The Lyapunov Exponents of Hyperbolic Measures for $C^1$ Vector Fields with Dominated Splitting},
author = {Wanlou Wu},
journal= {arXiv preprint arXiv:2512.24911},
year = {2026}
}