By Jorge Ize

This paintings is dedicated to an in depth learn of the equivariant measure and its functions for the case of an $S^1$-action. This measure is a component of the equivariant homotopy workforce of spheres, that are computed in a step by step extension technique. functions contain the index of an remoted orbit, branching and Hopf bifurcation, and interval doubling and symmetry breaking for platforms of self sustaining differential equations. The authors have paid designated cognizance to creating the textual content as self-contained as attainable, in order that the one historical past required is a few familiarity with the fundamental principles of homotopy idea and of Floquet thought in differential equations. Illustrating in a typical manner the interaction among topology and research, this booklet should be of curiosity to researchers and graduate scholars.

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