Hausdorff dimension for horseshoes in ℝ3

Károly Simon, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

Using pressure formulas we compute the Hausdorff dimension of the basic set of 'almost every' C1+α horseshoe map in ℝ3 of the form F(x, y, z) = (γ(x, z), τ(y, z), ψ(z)), where |ψ′| > 1 and 0 < |γ′x|, |τ′y| < 1/2 on the basic set. Similar results are obtained for attractors of nonlinear 'baker's maps' in ℝ3.

Original languageEnglish
Pages (from-to)1343-1363
Number of pages21
JournalErgodic Theory and Dynamical Systems
Volume19
Issue number5
DOIs
StatePublished - Oct 1999
Externally publishedYes

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