Degree Theory for Equivariant Maps, the General $S^1$-Action
Author: Jorge Ize
Publisher: American Mathematical Soc.
Published: 1992
Total Pages: 194
ISBN-13: 0821825429
DOWNLOAD EBOOKIn 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.