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Differentiable Dynamical Systems: An Introduction to Structural Stability and Hyperbolicity

Lan Wen Peking University, Beijing, China
Available Formats:
Hardcover ISBN: 978-1-4704-2799-3
Product Code: GSM/173
List Price: $79.00 MAA Member Price:$71.10
AMS Member Price: $63.20 Electronic ISBN: 978-1-4704-3210-2 Product Code: GSM/173.E List Price:$79.00
MAA Member Price: $71.10 AMS Member Price:$63.20
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List Price: $118.50 MAA Member Price:$106.65
AMS Member Price: $94.80 Click above image for expanded view Differentiable Dynamical Systems: An Introduction to Structural Stability and Hyperbolicity Lan Wen Peking University, Beijing, China Available Formats:  Hardcover ISBN: 978-1-4704-2799-3 Product Code: GSM/173  List Price:$79.00 MAA Member Price: $71.10 AMS Member Price:$63.20
 Electronic ISBN: 978-1-4704-3210-2 Product Code: GSM/173.E
 List Price: $79.00 MAA Member Price:$71.10 AMS Member Price: $63.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$118.50 MAA Member Price: $106.65 AMS Member Price:$94.80
• Book Details

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.

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

• 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 reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
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.

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 reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
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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