Degree theory for equivariant maps, the general S[1]-action
著者
書誌事項
Degree theory for equivariant maps, the general S[1]-action
（Memoirs of the American Mathematical Society, no. 481）
American Mathematical Society, 1992
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注記
Includes bibliographical references (p. 177-179)
"November 1992, volume 100, number 481 (end of volume)"
内容説明・目次
内容説明
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.
目次
Preliminaries Extensions of $S^1$-maps Homotopy groups of $S^1$-maps Degree of $S^1$-maps $S^1$-index of an isolated non-stationary orbit and applications Index of an isolated orbit of stationary solutions and applications Virtual periods and orbit index Appendix: Additivity up to one suspension.
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