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The Lyapunov exponents of C 1 hyperbolic systems

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Abstract

Let f be a C 1 diffeomorphisim of smooth Riemannian manifold and preserve a hyperbolic ergodic measure µ. We prove that if the Osledec splitting is dominated, then the Lyapunov exponents of µ can be approximated by the exponents of atomic measures on hyperbolic periodic orbits.

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Authors and Affiliations

  1. College of Mathematics and Physics, Chongqing University, Chongqing, 400044, China

    YunHua Zhou

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    WenXiang Sun

Authors
  1. YunHua Zhou
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  2. WenXiang Sun
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Correspondence to YunHua Zhou.

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Zhou, Y., Sun, W. The Lyapunov exponents of C 1 hyperbolic systems. Sci. China Math. 53, 1743–1752 (2010). https://doi.org/10.1007/s11425-010-3117-5

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  • DOI: https://doi.org/10.1007/s11425-010-3117-5

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