The Lyapunov exponents of C1 hyperbolic systems

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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Bibliographic Details
Published in:Science China. Mathematics 2010, Vol.53 (7), p.1743-1752
Main Authors: Zhou, YunHua, Sun, WenXiang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-010-3117-5