Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Degree Theory for Equivariant Maps, the General $S^1$-Action
 
Degree Theory for Equivariant Maps, the General $S^1$-Action
eBook ISBN:  978-1-4704-0058-3
Product Code:  MEMO/100/481.E
List Price: $38.00
MAA Member Price: $34.20
AMS Member Price: $22.80
Degree Theory for Equivariant Maps, the General $S^1$-Action
Click above image for expanded view
Degree Theory for Equivariant Maps, the General $S^1$-Action
eBook ISBN:  978-1-4704-0058-3
Product Code:  MEMO/100/481.E
List Price: $38.00
MAA Member Price: $34.20
AMS Member Price: $22.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1001992; 179 pp
    MSC: Primary 58; Secondary 34; 47; 54; 55;

    This work is devoted to a detailed study of the equivariant degree and its applications for the case of an \(S^1\)-action. This degree is an element of the equivariant homotopy group of spheres, which are computed in a step-by-step extension process. Applications include the index of an isolated orbit, branching and Hopf bifurcation, and period doubling and symmetry breaking for systems of autonomous differential equations. The authors have paid special attention to making the text as self-contained as possible, so that the only background required is some familiarity with the basic ideas of homotopy theory and of Floquet theory in differential equations. Illustrating in a natural way the interplay between topology and analysis, this book will be of interest to researchers and graduate students.

    Readership

    Researchers and graduate students who wish to learn about the interplay between topology and analysis.

  • Table of Contents
     
     
    • Chapters
    • 1. Preliminaries
    • 2. Extensions of $S^1$-maps
    • 3. Homotopy groups of $S^1$-maps
    • 4. Degree of $S^1$-maps
    • 5. $S^1$-index of an isolated non-stationary orbit and applications
    • 6. Index of an isolated orbit of stationary solutions and applications
    • 7. Virtual periods and orbit index
    • Appendix. Additivity up to one suspension
  • 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: 1001992; 179 pp
MSC: Primary 58; Secondary 34; 47; 54; 55;

This work is devoted to a detailed study of the equivariant degree and its applications for the case of an \(S^1\)-action. This degree is an element of the equivariant homotopy group of spheres, which are computed in a step-by-step extension process. Applications include the index of an isolated orbit, branching and Hopf bifurcation, and period doubling and symmetry breaking for systems of autonomous differential equations. The authors have paid special attention to making the text as self-contained as possible, so that the only background required is some familiarity with the basic ideas of homotopy theory and of Floquet theory in differential equations. Illustrating in a natural way the interplay between topology and analysis, this book will be of interest to researchers and graduate students.

Readership

Researchers and graduate students who wish to learn about the interplay between topology and analysis.

  • Chapters
  • 1. Preliminaries
  • 2. Extensions of $S^1$-maps
  • 3. Homotopy groups of $S^1$-maps
  • 4. Degree of $S^1$-maps
  • 5. $S^1$-index of an isolated non-stationary orbit and applications
  • 6. Index of an isolated orbit of stationary solutions and applications
  • 7. Virtual periods and orbit index
  • Appendix. Additivity up to one suspension
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.