Verbitskij, E. A.; Takens, F. Generalized entropies. (English. Russian original) Zbl 0929.37001 Math. Notes 63, No. 1, 112-115 (1998); translation from Mat. Zametki 63, No. 1, 127-130 (1998). The purpose of this note is to study Renyi entropies from the ergodic theory viewpoint. Applications of the Renyi entropies to dynamical systems seem to have first appeared in the physical literature in order to define chaotic behaviour numerically. Here the authors present an elegant and mathematically rigorous approach to Renyi entropies. Reviewer: Messoud Efendiev (Berlin) Cited in 1 Document MSC: 37A25 Ergodicity, mixing, rates of mixing 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory Keywords:generalized entropy; correlation integral; Renyi entropies; ergodic theory; chaotic behaviour PDFBibTeX XMLCite \textit{E. A. Verbitskij} and \textit{F. Takens}, Math. Notes 63, No. 1, 112--115 (1998; Zbl 0929.37001); translation from Mat. Zametki 63, No. 1, 127--130 (1998) Full Text: DOI References: [1] G. E. Hentschel and I. Procaccia,Phys. D,8, 435–444 (1983). · Zbl 0538.58026 [2] J.-P. Eckmann and D. Ruelle,Rev. Modern Phys.,57, No. 3, 365 (1985). [3] P. Grassberger and I. Procaccia,Phys. Rev. A (3),28, 2591–2593 (1983). [4] Ya. G. Sinai,Mat. Sb. [Math. USSR-Sb.],63, No. 1, 23–42 (1964). [5] A. Renyi,Probability Theory, North-Holland, Amsterdam (1970). [6] M. Brin and A. Katok, ”On local entropy,” in:Geometric Dynamics, Vol. 1007, Lecture Notes in Math., Springer, New York (1983), pp. 30–38. · Zbl 0533.58020 [7] R. Bowen,Methods of Symbolic Dynamics [Russian translation], Vol. 13, New Advances in Foreign Science. Mathematics, Mir, Moscow (1979). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.