Authors
Citation
K. Simon et F. Solomyak, Hausdorff dimension for horseshoes in R-3, ERGOD TH DY, 19, 1999, pp. 1343-1363
Citations number
33
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
01433857
→ ACNP
Volume
19
Year of publication
1999
Part
5
Pages
1343 - 1363
Database
ISI
SICI code
0143-3857(199910)19:<1343:HDFHIR>2.0.ZU;2-M
Abstract
Using pressure formulas we compute the Hausdorff dimension of the basic set
of 'almost every' C1+alpha horseshoe map in R-3 of the form F(x, y, z) (y(
x, z), tau(y, z), psi (z)), where \psi\ > 1 and 0 < \y'(x)\, \tau'(y)\ < 1/
2 on the basic set. Similar results are obtained for attractors of nonlinea
r 'baker's maps' in R-3.