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

Download or read book Degree Theory for Equivariant Maps, the General $S^1$-Action written by Jorge Ize and published by American Mathematical Soc.. This book was released on 1992 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we consider general [italic]S1-actions, which may differ on the domain and on the range, with isotropy subspaces with one dimension more on the domain. In the special case of self-maps the [italic]S1-degree is given by the usual degree of the invariant part, while for one parameter [italic]S1-maps one has an integer for each isotropy subgroup different from [italic]S1. In particular we recover all the [italic]S1-degrees introduced in special cases by other authors and we are also able to interpret period doubling results on the basis of our [italic]S1-degree. The applications concern essentially periodic solutions of ordinary differential equations.