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The Hausdorff dimension of the set of dissipative points for a Cantor-like model set of singly cusped parabolic dynamics

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Author

Summary, in English

In this paper we introduce and study a certain intricate Cantor-like set C contained in unit interval. Our main result is to show that the set C itself, as well as the set of dissipative points within C, both have Hausdorff dimension equal to 1. The proof uses the transience of a certain non-symmetric Cauchy-type random walk.

Department/s

Publishing year

2009

Language

English

Pages

179-196

Publication/Series

Kodai Mathematical Journal

Volume

32

Issue

2

Document type

Journal article

Publisher

Kinokuniya Co Ltd

Topic

  • Mathematics

Keywords

  • Hausdorff dimension
  • Fractal geometry
  • Cauchy random walks
  • Kleinian
  • groups

Status

Published

Research group

  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 0386-5991