Newhouse, Sheldon E. Continuity properties of entropy. (English) Zbl 0676.58039 Ann. Math. (2) 129, No. 2, 215-235 (1989). 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 Cited in 7 ReviewsCited in 113 Documents MSC: 37A99 Ergodic theory Keywords:local entropy; topological and metric entropies; hyperbolic measures PDFBibTeX XMLCite \textit{S. E. Newhouse}, Ann. Math. (2) 129, No. 2, 215--235 (1989; Zbl 0676.58039) Full Text: DOI