Morse Theory for Symmetric Functionals on the Sphere and an Application to a Bifurcation Problem.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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
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