Multifractal Analysis of Dimensions and Entropies

F. Takens*, E. Verbitski

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademic

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    Abstract

    The theory of dynamical systems has undergone a dramatical revolution in the 20th century. The beauty and power of the theory of dynamical systems is that it links together different areas of mathematics and physics. In the last 30 years a great deal of attention was dedicated to a statistical description of strange attractors. This led to the development of notions of various dimensions and entropies, which can be associated to the attractor, dynamical system or invariant measure. In this paper we review these notions and discuss relations between those, among which the most prominent is the so-called multifractal formalism.
    Original languageEnglish
    Pages (from-to)361-382
    Number of pages22
    JournalRegular & chaotic dynamics
    Volume5
    Issue number4
    DOIs
    Publication statusPublished - 2000

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