Smooth Ergodic Theory for Endomorphisms

1. Auflage 2009
ISBN: 978-3-642-01953-1
Verlag: Springer

Buch, Englisch, Band 1978, 277 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 940 g

Reihe: Lecture Notes in Mathematics

Smooth ergodic theory of deterministic dynamical systems deals with the study of dynamical behaviors relevant to certain invariant measures under differentiable mappingsor ows. The relevance of invariantmeasures is that they describe the f- quencies of visits for an orbit and hence they give a probabilistic description of the evolution of a dynamical system. The fact that the system is differentiable allows one to use techniques from analysis and geometry. The study of transformationsand their long-termbehavior is ubiquitousin ma- ematics and the sciences. They arise not only in applications to the real world but also to diverse mathematical disciplines, including number theory, Lie groups, - gorithms, Riemannian geometry, etc. Hence smooth ergodic theory is the meeting ground of many different ideas in pure and applied mathematics. It has witnessed a great progress since the pioneering works of Sinai, Ruelle and Bowen on Axiom A diffeomorphisms and of Pesin on non-uniformly hyperbolic systems, and now it becomes a well-developed eld.

Zielgruppe

Research

Autoren/Hrsg.

Qian, Min

Xie, Jian-Sheng

Zhu, Shu

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Preliminaries.- Margulis-Ruelle Inequality.- Expanding Maps.- Axiom A Endomorphisms.- Unstable and Stable Manifolds for Endomorphisms.- Pesin#x2019;s Entropy Formula for Endomorphisms.- SRB Measures and Pesin#x2019;s Entropy Formula for Endomorphisms.- Ergodic Property of Lyapunov Exponents.- Generalized Entropy Formula.- Exact Dimensionality of Hyperbolic Measures.