Continuity properties of entropy (Q1122848)

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.