Piecewise linear maps, Liapunov exponents and entropy |
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Authors: | Jonq Juang |
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Affiliation: | a Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan b Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan |
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Abstract: | Let be a class of piecewise linear maps associated with a transition matrix A. In this paper, we prove that if fA,x∈LA, then the Liapunov exponent λ(x) of fA,x is equal to a measure theoretic entropy hmA,x of fA,x, where mA,x is a Markov measure associated with A and x. The Liapunov exponent and the entropy are computable by solving an eigenvalue problem and can be explicitly calculated when the transition matrix A is symmetric. Moreover, we also show that maxxλ(x)=maxxhmA,x=log(λ1), where λ1 is the maximal eigenvalue of A. |
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Keywords: | Piecewise linear map Liapunov exponents Entropy Ergodic theory |
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