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Fractal Structure of Conformal Expanding Random Repellers

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2036)

Abstract

We now deal with conformal expanding random maps. We prove an appropriate version of Bowen’s Formula, which asserts that the Hausdorff dimension of almost every fiber \({\mathcal{J}}_{x}\), denoted throughout the paper by \(\mathrm{HD}\), is equal to a unique zero of the function \(t\mapsto \mathcal{E}\!P(t)\).

Keywords

  • Hausdorff Dimension
  • Hausdorff Measure
  • Packing Measure
  • Random System
  • Unique Zero

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Correspondence to Volker Mayer .

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© 2011 Springer-Verlag Berlin Heidelberg

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Mayer, V., Skorulski, B., Urbanski, M. (2011). Fractal Structure of Conformal Expanding Random Repellers. In: Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry. Lecture Notes in Mathematics(), vol 2036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23650-1_5

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