Bowen’s Formula for the Hausdorff Dimension of Self-Similar Sets

  • David Ruelle
Part of the Progress in Physics book series (PMP, volume 7)


Geometric self-similarity of a set J (with a metric) means that the microscopic structure of the set (in any neighborhood of any point) can be magnified to ressemble the macroscopic structure of the set. The Hausdorff dimension t of J is then a natural notion, as stressed by Mandelbrot [5]. Bowen’s formula expresses t in terms of concepts of statistical mechanics, and can be used to show that the dimension t is not an integer (see Bowen [3]) or that it depends smoothly on parameters (see Ruelle [7]).


Hausdorff Dimension Gibbs Measure Admissible Sequence Markov Partition Macroscopic Structure 
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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • David Ruelle

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