# Accession Number:

## ADA046493

# Title:

## Generalized Cohomological Index Theories for Lie Group Actions with an Application to Bifurcation Questions for Hamiltonian Systems.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1977-07-01

# Pagination or Media Count:

## 74.0

# Abstract:

A general index theory for Lie group actions is developed which applies in particular to subsets of a Banach space which are invariant under the action of a compact Lie group G. Important special cases occur when G is Z2 or Ssuperscript 1. This theory should be useful for problems involving differential equations which are invariant under G, in particular in obtaining estimates for the the number of solutions of these equations. As an application a bifurcation problem for Hamiltonian systems of ordinary differential equations is studied and estimates are made on the number of periodic solutions bifurcating from an equilibrium solution. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics