Differentiable Dynamical Systems

An Introduction to Structural Stability and Hyperbolicity

AvLan Wen

Inbunden, Engelska, 2016

Del i serien Graduate Studies in Mathematics

1 586 kr

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Beskrivning

This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale.While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study.

Produktinformation

Utgivningsdatum:2016-07-30
Mått:178 x 254 x undefined mm
Vikt:526 g
Format:Inbunden
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:192
Förlag:American Mathematical Society
ISBN:9781470427993

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Lan Wen, Peking University, Beijing, China.

Recensioner i media

This book introduces the reader to some basic concepts of hyperbolic theory of dynamical systems with emphasis on structural stability. It is well written, the proofs are presented with great attention to details, and every chapter ends with a good collection of exercises. It is suitable for a semester-long course on the basics of dynamical systems"". - Yakov Pesin, Penn State University""Lan Wen's book is a thorough introduction to the ``classical'' theory of (uniformly) hyperbolic dynamics, updated in light of progress since Smale's seminal 1967 Bulletin article. The exposition is aimed at newcomers to the field and is clearly informed by the author's extensive experience teaching this material. A thorough discussion of some canonical examples and basic technical results culminates in the proof of the Omega-stability theorem and a discussion of structural stability. A fine basic text for an introductory dynamical systems course at the graduate level"". - Zbigniew Nitecki, Tufts University"...[T]he introductory parts of the book are quite suitable for graduate students, and the more advanced sections can be useful even for experts in the field." - S. Yu. Pilyugin, Mathematical Reviews

Innehållsförteckning

Basics of dynamical systemsHyperbolic fixed pointsHorseshoes, toral automorphisms, and solenoidsHyperbolic setsAxiom A, no-cycle condition, and Ω-stabilityQuasi-hyperbolicity and linear transversalityBibliographyIndex