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

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 Z(2) or S(superscript 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)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1977
Accession Number
ADA046493

Entities

People

  • Edward R. Fadell
  • Paul Rabinowitz

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algebraic Topology
  • Banach Space
  • Calculus
  • Calculus Of Variations
  • Complex Numbers
  • Contracts
  • Differential Equations
  • Eigenvalues
  • Equations
  • Geometry
  • Lie Groups
  • Mathematics
  • Military Research
  • Periodic Functions
  • Topology
  • United States
  • Variational Methods

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.

Technology Areas

  • Space