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Second Variational Formulae for Dimension Spectra

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Abstract

Consider basic set for Axiom A diffeomorphism on compact surface.We derive second variational formulae for the dimension spectra of equilibrium state on the basic set with respect to the perturbations of both the potential and\break the dynamical system.In particular we obtain a second variational formula for the Hausdorff dimension of the basic set.These results will find their use in the study of a quadratic extremal problem for multifrcatal analysis.

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Authors and Affiliations

  1. Department of Mathematics,Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan

    Michihiro Hirayama

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  1. Michihiro Hirayama
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Correspondence to Michihiro Hirayama.

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Hirayama, M. Second Variational Formulae for Dimension Spectra. J Stat Phys 118, 103–118 (2005). https://doi.org/10.1007/s10955-004-8779-3

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  • DOI: https://doi.org/10.1007/s10955-004-8779-3

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