# Accession Number:

## ADA141709

# Title:

## Morse Theory for Symmetric Functionals on the Sphere and an Application to a Bifurcation Problem.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1984-04-01

# Pagination or Media Count:

## 22.0

# Abstract:

This paper uses Conleys 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 A0 is given. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics