Hausdorff dimension for horseshoes-Reference-Cited by-同舟云学术

Hausdorff dimension for horseshoes

Published:1983-06 Issue:2 Volume:3 Page:251-260
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

McCluskey Heather,Manning Anthony

Abstract

AbstractWe shall measure how thick a basic set of a C1 axiom A diffeomorphism of a surface is by the Hausdorff dimension of its intersection with an unstable manifold. This depends continuously on the diffeomorphism. Generically a C2 diffeomorphism has attractors whose Hausdorff dimension is not approximated by the dimension of its ergodic measures.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference20 articles.

1. Dimension, entropy and Lyapunov exponents

2. A Variational Principle for the Pressure of Continuous Transformations

3. Differentiable dynamical systems

4. A formula for the Hausdorff dimension of a two-dimensional hyperbolic attractor;Pesin;Funk. Anal. i ego Prilozh,1982

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