Equivariant Conley index  versus degree for equivariant gradient maps

Anna Go??biewska; S?awomir Rybicki

doi:10.3934/dcdss.2013.6.985

Article Contents

2013, Volume 6, Issue 4: 985-997. Doi: 10.3934/dcdss.2013.6.985

This issue Previous Article Bifurcation of periodic solutions from a ring configuration of discrete nonlinear oscillators Next Article Unbounded sequences of cycles in general autonomous equations with periodic nonlinearities

Equivariant Conley index versus degree for equivariant gradient maps

Anna Go??biewska^1,2,3, and
S?awomir Rybicki^1,2,3,

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

Received: September 30, 2011

Revised: March 31, 2012

Published: July 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 37G40; Secondary: 58E09.

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