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A proof of the estimation from below in Pesin’s entropy formula. (English) Zbl 0533.58022
The authors prove part of the Pesin entropy formula in the following general form: let M be a compact Riemannian manifold, and let \(\Phi\) be a diffeomorphism of M of class \(C^{1+\epsilon}\), or else a map with singularities of the kind considered by Katok and the second author (1981). Let \(\mu\) be a measure on M which is absolutely continuous with respect to the global unstable foliation of \(\Phi\). Then the metric entropy of the system \((M,\mu\),\(\Phi)\) is equal to the integral over M, with respect to \(d\mu\) (x), of the sum of the positive Lyapunov characteristic exponents at x. (The authors actually prove only the ”\(\geq ''\) part.)
Reviewer: R.Darling

MSC:
37A99 Ergodic theory
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