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Invariant Measures Satisfying an Equality Relating Entropy, Folding Entropy and Negative Lyapunov Exponents

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Abstract

In this paper we prove that, for a C 2 (non-invertible but non-degenerate) map on a compact manifold, an invariant measure satisfies an equality relating entropy, folding entropy and negative Lyapunov exponents if and, under a condition on the Jacobian of the map, only if the measure has absolutely continuous conditional measures on the stable manifolds.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Pei-Dong Liu

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  1. Pei-Dong Liu
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Correspondence to Pei-Dong Liu.

Additional information

Communicated by G. Gallavotti

This work is supported by National Basic Research Program of China (973 Program) (2007CB814800).

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Liu, PD. Invariant Measures Satisfying an Equality Relating Entropy, Folding Entropy and Negative Lyapunov Exponents. Commun. Math. Phys. 284, 391–406 (2008). https://doi.org/10.1007/s00220-008-0568-4

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