Hausdorff dimension for some hyperbolic attractors with overlaps and without finite Markov partition

Franz Hofbauer, Peter Raith, Károly Simon

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper some families of skew product self-maps F on the square are considered. The main example is a family forming a two-dimensional analogue of the tent map family. According to the assumptions made in this paper these maps are almost injective. This means that the points of the attractor having more than one inverse image form a set of measure zero for all interesting measures. It may be that F does not have a finite Markov partition. The Hausdorff dimension of the attractor is computed.

Original languageEnglish
Pages (from-to)1143-1165
Number of pages23
JournalErgodic Theory and Dynamical Systems
Volume27
Issue number4
DOIs
Publication statusPublished - Aug 1 2007

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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