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

Jörg Schmeling, Bernd Stratmann

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)179-196
JournalKodai Mathematical Journal
Volume32
Issue number2
DOIs
Publication statusPublished - 2009

Subject classification (UKÄ)

  • Mathematics

Free keywords

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

Fingerprint

Dive into the research topics of 'The Hausdorff dimension of the set of dissipative points for a Cantor-like model set of singly cusped parabolic dynamics'. Together they form a unique fingerprint.

Cite this