EQUIVARIANT CONLEY INDEX VERSUS DEGREE FOR EQUIVARIANT GRADIENT MAPS

摘要

In this article we study the relationship between the degree for invariant strongly indefinite functionals and the equivariant Conley index. We prove that, under certain assumptions, a change of the equivariant Conley indices is equivalent to the change of the degrees for equivariant gradient maps. Moreover, we formulate easy to verify sufficient conditions for the existence of a global bifurcation of critical orbits of invariant strongly indefinite functionals.