Generalized entropies: Renyi and correlation integral approach

E.A. Verbitskii, F. Takens

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    Abstract

    We study the generalized Renyi entropies which were introduced in the physics literature. The proper defintion of these entropies needs, in our opinion, further clarification. We show that the Renyi entropies do not contain any new information. On the other hand, we introduce the notion of the correlation entropies, which are not invariants of the dynamical systems in the measure-theoretic sense, but they are invariant under transformations of the state space with bounded distortion. With these correlation entropies we provide a formal definition which can serve as a basis for the results reported in the physics literature.

    Original languageEnglish
    Pages (from-to)771-782
    Number of pages12
    JournalMathematical notes
    Volume63
    Issue number1-2
    Publication statusPublished - Jul-1998

    Keywords

    • STRANGE ATTRACTORS
    • PHASE-TRANSITIONS
    • CHAOTIC SYSTEMS
    • DIMENSIONS
    • SETS

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