What type of study is this?

This is a Quantitative Study study.

October 9, 2025Open Access

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

Key Points

Ergodic hyperbolic invariant measures can be approximated by periodic measures.
Lyapunov exponents of ergodic hyperbolic invariant measures approximate those of periodic measures.
The study focuses on C1 star vector fields and three-dimensional manifolds.
Results provide important insights for understanding dynamics in vector fields.

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.

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Cite This Study

Lu et al. (Thu,) studied this question.

synapsesocial.com/papers/68e7103b90569dd607ee6961 https://doi.org/https://doi.org/10.48550/arxiv.2507.23605

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