Dynamics Beyond Uniform Hyperbolicity

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.

From the reviews:

"... Nonuniformly hyperbolic phenomena are a central theme in current research in dynamical systems theory. The attractive book under review is meant as a guide for students as well as established researchers to explore these new and exciting ideas.  ...

The book is well written by recognized expers who have made significant contributions to their subject. They have wisely chosen to make the various sections of their book essentially self-contained. Thus, the narrative is suitable for cover-to-cover exploration or more concentrated study of specific topics. While definiotions and theorems are stated precisely, only outlines of most of the proofs are given; the reader is referred (via a bibliography with 466 entries) to the research literature for details. This practice sets the style for the book: The main ideas are front and center, where they should be for the current state of the subject to come rapidly into focus. Students - young and old - will find here a broad and insightful overview of recent results in modern dynamical systems theory, where many open problems and future directions for research are discussed. ...

The authors have good reason to believe that many readers will be inspired by their excellent book."

Carmen Chicone, Univ. of Missouri-Columbia, Siam Review, Issue 47, No. 4, 2005

"The notion of uniform hyperbolicity led to the remarkable advances in the theory of dynamical systems in the 60ies and 70ies of the 20th century ... . The book is a welcome reference source for researchers and graduate students who work in or just want to get impression on this important and rapidly developing area of dynamical systems." (Yuri Kifer, Zentralblatt MATH, Vol. 1060, 2005)