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Author:   Christian Bonatti ,  Lorenzo J. Díaz ,  Marcelo Viana
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2005
Volume:   102
Dimensions:   Width: 15.50cm , Height: 2.10cm , Length: 23.50cm
Weight:   0.617kg
ISBN:  

9783642060410

ISBN 10:   3642060412
Pages:   384
Publication Date:   19 October 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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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.

Reviews

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)

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)

"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)"

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