Dynamics Beyond Uniform Hyperbolicity A Global Geometric and Probabilistic Perspective /

• Main Authors: Bonatti, Christian (Author), Díaz, Lorenzo J. (Author), Viana, Marcelo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.
• Series: Encyclopaedia of Mathematical Sciences, Mathematical Physics III, 102
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Dynamics.; Ergodic theory.; Physics.; Dynamical Systems and Ergodic Theory.; Analysis.; Mathematical Methods in Physics.

In broad terms, the goal of dynamics is to describe the long-term evolution of systems for which an "infinitesimal" evolution rule, such as a differential equation or the iteration of a map, is known. The notion of uniform hyperbolicity, introduced by Steve Smale in the early sixties, unif...

Table of Contents:

• Hyperbolicity and Beyond
• One-Dimensional Dynamics
• Homoclinic Tangencies
• Hénon-like Dynamics
• Non-Critical Dynamics and Hyperbolicity
• Heterodimensional Cycles and Blenders
• Robust Transitivity
• Stable Ergodicity
• Robust Singular Dynamics
• Generic Diffeomorphisms
• SRB Measures and Gibbs States
• Lyapunov Exponents.