Entropy formula for endomorphisms: Relations between entropy, exponents and dimension

Min Qian; Jian-Sheng Xie

doi:10.3934/dcds.2008.21.367

Article Contents

2008, Volume 21, Issue 2: 367-392. Doi: 10.3934/dcds.2008.21.367

This issue Previous Article Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets Next Article Axiom a systems without sinks and sources on $n$-manifolds

Entropy formula for endomorphisms: Relations between entropy, exponents and dimension

Min Qian^1, and
Jian-Sheng Xie^2,

1.
School of Mathematical Sciences, Peking University, Beijing 100871
2.
School of Mathematical Sciences, Fudan University, Shanghai 200433

Received: January 31, 2007

Revised: November 30, 2007

Published: April 2008

Abstract Related Papers Cited by

Abstract

We present an entropy formula of Ledrappier-Young type for invariant measures (maybe non-SRB) of $ C^2 $ endomorphisms (maybe non-invertible and with singularities) on a compact manifold via their inverse limit spaces. This result may be considered as the most general form of entropy formula for a deterministic system with an invariant measure, and a preliminary step to Eckmann-Ruelle conjecture. As an important application, we have proved the exact dimensionality of ergodic measures invariant under expanding maps.

Keywords:

Mathematics Subject Classification: Primary: 37C40, 37C45; Secondary: 37D20.

Citation:

Article Metrics

HTML views() PDF downloads(68) Cited by(0)

Entropy formula for endomorphisms: Relations between entropy, exponents and dimension

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Entropy formula for endomorphisms: Relations between entropy, exponents and dimension

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content