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Differentiable Dynamical Systems: An Introduction to Structural Stability and Hyperbolicity
 
Lan Wen Peking University, Beijing, China
Differentiable Dynamical Systems
Hardcover ISBN:  978-1-4704-2799-3
Product Code:  GSM/173
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-3210-2
Product Code:  GSM/173.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-2799-3
eBook: ISBN:  978-1-4704-3210-2
Product Code:  GSM/173.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
Differentiable Dynamical Systems
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Differentiable Dynamical Systems: An Introduction to Structural Stability and Hyperbolicity
Lan Wen Peking University, Beijing, China
Hardcover ISBN:  978-1-4704-2799-3
Product Code:  GSM/173
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-3210-2
Product Code:  GSM/173.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-2799-3
eBook ISBN:  978-1-4704-3210-2
Product Code:  GSM/173.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1732016; 192 pp
    MSC: Primary 37; 34

    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 \(\Omega\)-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.

    Ancillaries:

    Readership

    Graduate students and research mathematicians interested in the hyperbolic theory of dynamical systems.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Basics of dynamical systems
    • Chapter 2. Hyperbolic fixed points
    • Chapter 3. Horseshoes, toral automorphisms, and solenoids
    • Chapter 4. Hyperbolic sets
    • Chapter 5. Axiom A, no-cycle condition, and $\Omega $-stability
    • Chapter 6. Quasi-hyperbolicity and linear transversality
  • Reviews
     
     
    • ...[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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1732016; 192 pp
MSC: Primary 37; 34

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 \(\Omega\)-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.

Ancillaries:

Readership

Graduate students and research mathematicians interested in the hyperbolic theory of dynamical systems.

  • Chapters
  • Chapter 1. Basics of dynamical systems
  • Chapter 2. Hyperbolic fixed points
  • Chapter 3. Horseshoes, toral automorphisms, and solenoids
  • Chapter 4. Hyperbolic sets
  • Chapter 5. Axiom A, no-cycle condition, and $\Omega $-stability
  • Chapter 6. Quasi-hyperbolicity and linear transversality
  • ...[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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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