The Lyapunov Exponents of Hyperbolic Measures for C¹ Star Vector Fields on Three-dimensional Manifolds

2025/07/31 by Lu, Yuansheng, Wu, Wanlou
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.23605

Abstract

In this paper, we proved that for every C¹ star vector fields on three-dimensional manifolds, every ergodic hyperbolic invariant measure which is not supported on singularities 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.

Citations

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• A rescaled expansiveness for flows
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