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):

• Benci,V.
• Pacella,F.

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:

• *Bifurcation(Mathematics)
• *Points(Mathematics)
• Variational methods
• Hilbert space
• Symmetry
• Operators(Mathematics)
• Estimates
• Eigenvalues
• Spheres

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE