Skip to main content Accessibility help
×
×
Home

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

  • KÁROLY SIMON (a1) and BORIS SOLOMYAK (a2)

Abstract

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 $\mathbb{R}}^3$.

Copyright

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed