# American Institute of Mathematical Sciences

August  2013, 6(4): 985-997. doi: 10.3934/dcdss.2013.6.985

## Equivariant Conley index versus degree for equivariant gradient maps

 1 Faculty of Mathematics and Computer Science 2 Nicolaus Copernicus University 3 ul. Chopina 12/18, PL-87-100 Toru?

Received  October 2011 Revised  April 2012 Published  December 2012

In this article we study the relationship between the degree forinvariant strongly indefinite functionals and the equivariantConley index. We prove that, under certain assumptions, achange of the equivariant Conley indices is equivalent to thechange of the degrees for equivariant gradient maps. Moreover, weformulate easy to verify sufficient conditions for theexistence of a global bifurcation of critical orbits of invariantstrongly indefinite functionals.
Citation: Anna Go??biewska, S?awomir Rybicki. Equivariant Conley index versus degree for equivariant gradient maps. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 985-997. doi: 10.3934/dcdss.2013.6.985
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