Smooth Ergodic Theory for Endomorphisms

• Main Authors: Qian, Min. (Author), Xie, Jian-Sheng. (Author), Zhu, Shu. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1978
• Subjects: Mathematics.; Differentiable dynamical systems.; Mechanical engineering.; Dynamical Systems and Ergodic Theory.; Mechanical Engineering.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-01954-8

This volume presents a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms, mainly concerning the relations between entropy, Lyapunov exponents and dimensions. The authors make extensive use of the combination of the inverse limit space techniq...

Table of Contents:

• I Preliminaries
• II Margulis-Ruelle Inequality
• III Expanding Maps
• IV Axiom A Endomorphisms
• V Unstable and Stable Manifolds
• VI Pesins Entropy Formula
• VII SRB Measures and Entropy Formula
• VIII Ergodic Property of Lyapunov Exponents
• IX Generalized Entropy Formula
• X Dimension of Hyperbolic Measures.