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Degree Theory for Equivariant Maps, the General S¹-Action
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This work is devoted to a detailed study of the equivariant degree and its applications for the case of an S¹-action. This degree is an element of the equivariant homotopy group of spheres, which are computed in step-by-step extension process. Applications include the index of an isoloated 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 homoto...
This work is devoted to a detailed study of the equivariant degree and its applications for the case of an S¹-action. This degree is an element of the equivariant homotopy group of spheres, which are computed in step-by-step extension process. Applications include the index of an isoloated 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.
Table of contents:
Introduction; Preliminaries; Extensions of S¹-maps; Homotopy goups of S¹-maps; Degree of S¹-maps; S¹-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; References.
Table of contents:
Introduction; Preliminaries; Extensions of S¹-maps; Homotopy goups of S¹-maps; Degree of S¹-maps; S¹-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; References.