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Some characterizations of strange sets

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Abstract

A thermodynamic formalism is exhibited that is the canonical version of Halseyet al.'s microcanonical formulation. This formalism is applied to a four-scale Cantor set and it is shown that the singularity spectrum fails to uniquely encode the underlying dynamics.

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References

  1. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, to be published.

  2. D. Ruelle,Statistical Mechanics, Thermodynamic Formalism (Addison-Wesley, Reading, Massachusetts, 1978); E. B. Vul, Ya. G. Sinai, and K. M. Khanin,Uspekhi Mat. Nauk 39:3 (1984) [Russ. Math. Surv. 39:1 (1984)].

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Authors and Affiliations

  1. Division of Physics, Mathematics and Astronomy, California Institute of Technology, 91125, Pasadena, California

    Mitchell J. Feigenbaum

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  1. Mitchell J. Feigenbaum
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Feigenbaum, M.J. Some characterizations of strange sets. J Stat Phys 46, 919–924 (1987). https://doi.org/10.1007/BF01011148

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  • DOI: https://doi.org/10.1007/BF01011148

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