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May 27, 2026Ergodic Theory and Dynamical Systems0 citations

The Lyapunov exponents of hyperbolic measures for C 1 star vector fields on three-dimensional manifolds

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YLYu LuWWWanlou Wu

Key Points

  • The aim is to prove the approximation of ergodic hyperbolic invariant measures by periodic measures for C^1 star vector fields on 3D manifolds.
  • Proving the approximation of ergodic hyperbolic invariant measures not on singularities by periodic measures.
  • Investigating the relationship of Lyapunov exponents of invariant measures and periodic measures.
  • Every ergodic hyperbolic invariant measure can be approximated by periodic measures.
  • Lyapunov exponents of ergodic measures can be approximated by those of periodic measures.

Abstract

Abstract In this paper, we prove that for every C¹ star vector field on three-dimensional manifolds, every ergodic hyperbolic invariant measure which is not supported on singularities can be approximated by periodic measures and that 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. (2026) studied this question.

synapsesocial.com/papers/6a168a9c0c924ddd1bd59566https://doi.org/10.1017/etds.2026.10308
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