Periodic solutions of second order Hamiltonian systems bifurcating from infinity

Details Periodic solutions of second order Hamiltonian systems bifurcating from infinity Periodic solutions of second order Hamiltonian systems bifurcating from infinity

2006-04-12

arxiv.org/abs/math/0604284v1

Mathematics

Classical Analysis and ODEs

24 pages

Scientific paper

The goal of this article is to study closed connected sets of periodic solutions, of autonomous second order Hamiltonian systems, emanating from infinity. The main idea is to apply the degree for SO(2)-equivariant gradient operators defined by the second author. Using the results due to Rabier we show that we cannot apply the Leray-Schauder degree to prove the main results of this article. It is worth pointing out that since we study connected sets of solutions, we also cannot use the Conley index technique and the Morse theory.

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