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Degree Theory for Equivariant Maps, the General $S^1$-Action

Available Formats:
Electronic ISBN: 978-1-4704-0058-3
Product Code: MEMO/100/481.E
List Price: $38.00 MAA Member Price:$34.20
AMS Member Price: $22.80 Click above image for expanded view Degree Theory for Equivariant Maps, the General$S^1$-Action Available Formats:  Electronic 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.

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
• Requests

Review Copy – for reviewers who would like to review an AMS book
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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.

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 reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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