Continuity properties of entropy. (English) Zbl 0676.58039

Using the notion of local entropy, the author obtains an upper bound on the defect in uppersemicontinuity of the topological and metric entropies of \(C^ r\) self maps, \(r>1\), of \(C^ p\) manifolds, \(p>1\). For \(C^ r\) diffeomorphisms, \(r>1\), of positive entropy, necessary and sufficient conditions are given for the existence of hyperbolic measures of maximal entropy.
Reviewer: R.Cowen


37A99 Ergodic theory
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