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The General Topology of Dynamical Systems
 
Ethan Akin City College (CUNY), New York, NY
The General Topology of Dynamical Systems
Softcover ISBN:  978-0-8218-4932-3
Product Code:  GSM/1.S
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: July 01, 2024
eBook ISBN:  978-1-4704-2064-2
Product Code:  GSM/1.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Softcover ISBN:  978-0-8218-4932-3
eBook: ISBN:  978-1-4704-2064-2
Product Code:  GSM/1.S.B
List Price: $115.00 $87.50
MAA Member Price: $103.50 $78.75
AMS Member Price: $92.00 $70.00
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: July 01, 2024
The General Topology of Dynamical Systems
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The General Topology of Dynamical Systems
Ethan Akin City College (CUNY), New York, NY
Softcover ISBN:  978-0-8218-4932-3
Product Code:  GSM/1.S
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: July 01, 2024
eBook ISBN:  978-1-4704-2064-2
Product Code:  GSM/1.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Softcover ISBN:  978-0-8218-4932-3
eBook ISBN:  978-1-4704-2064-2
Product Code:  GSM/1.S.B
List Price: $115.00 $87.50
MAA Member Price: $103.50 $78.75
AMS Member Price: $92.00 $70.00
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: July 01, 2024
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 11993; 261 pp
    MSC: Primary 58; Secondary 34

    Topology, the foundation of modern analysis, arose historically as a way to organize ideas like compactness and connectedness which had emerged from analysis. Similarly, recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results (such as attractors, chain recurrence, and basic sets). This book collects these results, both old and new, and organizes them into a natural foundation for all aspects of dynamical systems theory. No existing book is comparable in content or scope. Requiring background in point-set topology and some degree of “mathematical sophistication”, Akin's book serves as an excellent textbook for a graduate course in dynamical systems theory. In addition, Akin's reorganization of previously scattered results makes this book of interest to mathematicians and other researchers who use dynamical systems in their work.

    Readership

    Graduate students and researchers in dynamical systems. Graduate-level textbook.

  • Table of Contents
     
     
    • Chapters
    • Chapter 0. Introduction: Gradient systems
    • Chapter 1. Closed relations and their dynamic extensions
    • Chapter 2. Invariant sets and Lyapunov functions
    • Chapter 3. Attractors and basic sets
    • Chapter 4. Mappings: Invariant subsets and transitivity concepts
    • Chapter 5. Computation of the chain recurrent set
    • Chapter 6. Chain recurrence and Lyapunov functions for flows
    • Chapter 7. Topologically robust properties of dynamical systems
    • Chapter 8. Invariant measures for mappings
    • Chapter 9. Examples: Circles, simplex, and symbols
    • Chapter 10. Fixed points
    • Chapter 11. Hyperbolic sets and axiom A homeomorphisms
    • Historical remarks
  • Reviews
     
     
    • No other single text has heretofore presented such a unified treatment of these topological ideas at this level of generality.

      Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 11993; 261 pp
MSC: Primary 58; Secondary 34

Topology, the foundation of modern analysis, arose historically as a way to organize ideas like compactness and connectedness which had emerged from analysis. Similarly, recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results (such as attractors, chain recurrence, and basic sets). This book collects these results, both old and new, and organizes them into a natural foundation for all aspects of dynamical systems theory. No existing book is comparable in content or scope. Requiring background in point-set topology and some degree of “mathematical sophistication”, Akin's book serves as an excellent textbook for a graduate course in dynamical systems theory. In addition, Akin's reorganization of previously scattered results makes this book of interest to mathematicians and other researchers who use dynamical systems in their work.

Readership

Graduate students and researchers in dynamical systems. Graduate-level textbook.

  • Chapters
  • Chapter 0. Introduction: Gradient systems
  • Chapter 1. Closed relations and their dynamic extensions
  • Chapter 2. Invariant sets and Lyapunov functions
  • Chapter 3. Attractors and basic sets
  • Chapter 4. Mappings: Invariant subsets and transitivity concepts
  • Chapter 5. Computation of the chain recurrent set
  • Chapter 6. Chain recurrence and Lyapunov functions for flows
  • Chapter 7. Topologically robust properties of dynamical systems
  • Chapter 8. Invariant measures for mappings
  • Chapter 9. Examples: Circles, simplex, and symbols
  • Chapter 10. Fixed points
  • Chapter 11. Hyperbolic sets and axiom A homeomorphisms
  • Historical remarks
  • No other single text has heretofore presented such a unified treatment of these topological ideas at this level of generality.

    Mathematical Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.