| 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 |
| 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 |
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Book DetailsGraduate Studies in MathematicsVolume: 173; 2016; 192 ppMSC: 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:
ReadershipGraduate students and research mathematicians interested in the hyperbolic theory of dynamical systems.
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Table of Contents
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Chapters
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Chapter 1. Basics of dynamical systems
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Chapter 2. Hyperbolic fixed points
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Chapter 3. Horseshoes, toral automorphisms, and solenoids
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Chapter 4. Hyperbolic sets
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Chapter 5. Axiom A, no-cycle condition, and $\Omega $-stability
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Chapter 6. Quasi-hyperbolicity and linear transversality
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Additional Material
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Reviews
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...[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
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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:
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
