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Hausdorff dimension of the singularities for invariant measures of expanding dynamical systems

Part of the Lecture Notes in Mathematics book series (LNM,volume 1331)

Abstract

We analyze the dimension spectrum introduced in [J.K.L.] to describe the local singularity of a measure. In the case of an invariant measure for an expanding Markov map of the interval, we show that this question can be studied by using large deviation theory and the associated Thermodynamic formalism.

Keywords

  • Partition Function
  • Invariant Measure
  • Hausdorff Dimension
  • Gibbs State
  • Thermodynamic Formalism

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1988 Springer-Verlag

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Collet, P. (1988). Hausdorff dimension of the singularities for invariant measures of expanding dynamical systems. In: Bamón, R., Labarca, R., Palis, J. (eds) Dynamical Systems Valparaiso 1986. Lecture Notes in Mathematics, vol 1331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083065

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  • DOI: https://doi.org/10.1007/BFb0083065

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  • Print ISBN: 978-3-540-50016-2

  • Online ISBN: 978-3-540-45889-0

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