## 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

### MSC:

 37A99 Ergodic theory
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