Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-15T01:58:49.164Z Has data issue: false hasContentIssue false
  • English
  • Français

Hausdorff dimension for horseshoes in $\mathbb{R}^3$

Published online by Cambridge University Press:  01 October 1999

KÁROLY SIMON and
BORIS SOLOMYAK
KÁROLY SIMON
Affiliation:
Institute of Mathematics, University of Miscolc, Miscolc-Egyetemváros, H-315, Hungary (e-mail:simon@gold.uni-miscolc.hu)
BORIS SOLOMYAK
Affiliation:
Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, USA (e-mail:solomyak@math.washington.edu)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Using pressure formulas we compute the Hausdorff dimension of the basic set of ‘almost every’ ${\cal C}^{1+\alpha}$ horseshoe map in$\mathbb{R}}^3$ of the form $F(x,y,z)= (\gamma(x,z), \tau(y,z), \psi(z))$, where $|\psi'|>1$ and $0< |\gamma'_x|, |\tau'_y| < \frac{1}{2}$ on the basic set. Similar results are obtained for attractors of nonlinear ‘baker's maps’ in $\mathbb{R}}^3$.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 5 , October 1999, pp. 1343 - 1363
Copyright
1999 Cambridge University Press