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Exponential closing property and approximation of Lyapunov exponents of linear cocycles
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Xiongping Dai
Published/Copyright:
April 2, 2011
Abstract
Let 
be a Hölder-continuous linear cocycle with a discrete-time, μ-measure-preserving driving flow ƒ: X × ℤ → X on a compact metric space X. We show that the Lyapunov characteristic spectrum of (
, μ) can be approached arbitrarily by that of periodic points. Consequently, if all periodic points have only nonzero Lyapunov exponents and such exponents are uniformly bounded away from zero, then (, μ) also has only non-zero Lyapunov exponents. In our arguments, an exponential closing property of the driving flow is a basic condition. And we prove that every C1-class diffeomorphism of a closed manifold obeys this closing property on its any hyperbolic invariant subsets.
Keywords.: Exponential closing; linear cocycle; Katok closing lemma; approximation of Lyapunov exponents and ergodic measures
Received: 2008-10-09
Revised: 2009-04-25
Published Online: 2011-04-02
Published in Print: 2011-March
© de Gruyter 2011
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- Topological types of 3-dimensional small covers
- Null controllability with constraints on the state for nonlinear heat equations
- Exponential closing property and approximation of Lyapunov exponents of linear cocycles
- Reflection systems and partial root systems
- Todd's maximum-volume ellipsoid problem on symmetric cones
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Keywords for this article
Exponential closing;
linear cocycle;
Katok closing lemma;
approximation of Lyapunov exponents and ergodic measures
Articles in the same Issue
- On the ampleness of the normal bundle of line congruences
- Topological types of 3-dimensional small covers
- Null controllability with constraints on the state for nonlinear heat equations
- Exponential closing property and approximation of Lyapunov exponents of linear cocycles
- Reflection systems and partial root systems
- Todd's maximum-volume ellipsoid problem on symmetric cones
- Refinement of the spectral asymptotics of generalized Krein Feller operators
