Smooth Ergodic Theory for Endomorphisms

Resource Information

The work Smooth Ergodic Theory for Endomorphisms represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.

Label

Smooth Ergodic Theory for Endomorphisms

Statement of responsibility

by Min Qian, Jian-Sheng Xie, Shu Zhu

Creator

• Qian, Min

Contributor

• Xie, Jian-Sheng.
• Zhu, Shu.
• SpringerLink

Author

• Zhu, Shu.
• Xie, Jian-Sheng.
• Qian, Min

Provider

• SpringerLink

Subject

• Mechanical Engineering
• Mechanical engineering
• Mathematics
• Differentiable dynamical systems
• Electronic resources
• Dynamical Systems and Ergodic Theory

Language

eng

Summary

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 technique and the techniques developed to tackle random dynamical systems. The most interesting results in this book are (1) the equivalence between the SRB property and Pesin’s entropy formula; (2) the generalized Ledrappier-Young entropy formula; (3) exact-dimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exact-dimensionality for weakly hyperbolic diffeomorphisms seems more accessible than that of Barreira et al. It also inspires the authors to argue to what extent the famous Eckmann-Ruelle conjecture and many other classical results for diffeomorphisms and for flows hold true. After a careful reading of the book, one can systematically learn the Pesin theory for endomorphisms as well as the typical tricks played in the estimation of the number of balls of certain properties, which are extensively used in Chapters IX and X

Member of

• Lecture Notes in Mathematics,, 1978

Image bit depth

0

LC call number

QA313

Literary form

non fiction

Series statement

Lecture Notes in Mathematics,

Series volume

1978