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Pressure and Dimension

  • Luís Barreira
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this chapter we recall in a pragmatic manner all the necessary notions and results from the thermodynamic formalism and dimension theory. In particular, we introduce the notions of topological pressure, BS-dimension, Hausdorff dimension, lower and upper box dimensions and pointwise dimension. We emphasize that we consider the general case of the topological pressure for noncompact sets, which is crucial in multifractal analysis.

Keywords

Hausdorff Dimension Topological Entropy Equilibrium Measure Dimension Theory Multifractal Analysis 
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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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Luís Barreira
    • 1
  1. 1.Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal

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