Morse Theory for Symmetric Functionals on the Sphere and an Application to a Bifurcation Problem.
Abstract
This paper uses Conley's index to study the cortical points of a function f on a finite dimensional sphere in presence of a symmetry group. The authors prove a theorem which leads to a lower bound on the number of critical points of f when the group is finite, even if the action is not free. This investigation has been motivated by the following bifurcation problem Au = lambda, where A is a variational G-equivariant operator. An estimated on the number of 'branches' bifurcating from an eigenvalue of A'(0) is given. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1984
- Accession Number
- ADA141709
Entities
People
- F. Pacella
- V. Benci
Organizations
- University of Wisconsin–Madison