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A dynamical system with integer information dimension and fractal correlation exponent

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Abstract

In this paper we construct a family {T γ}, 0<γ<1/2, of exact endomorphisms of [0, 1] such that the invariant measurem γ ofT γ is equivalent to Lebesgue measure but has fractal correlation exponent ν=2γ. This shows that an almost complete dichotomy can exist between the information dimension and the correlation exponent in observable dynamical systems.

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    C. D. Cutler

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  1. C. D. Cutler
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Communicated by J.-P. Eckmann

Research supported by the Natural Sciences and Engineering Research Council of Canada

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Cutler, C.D. A dynamical system with integer information dimension and fractal correlation exponent. Commun.Math. Phys. 129, 621–629 (1990). https://doi.org/10.1007/BF02097108

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  • DOI: https://doi.org/10.1007/BF02097108

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