Bifurcation of heteroclinic orbits via an index theory

2017/04/22 by Hu, Xijun, Portaluri, Alessandro · 1 citation
#34C37 #37C29 #47J15 #53D12 #70K44 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.06806

Abstract

Heteroclinic orbits for one-parameter families of nonautonomous vectorfields appear in a very natural way in many physical applications. Inspired by some recent bifurcation results for homoclinic trajectories of nonautonomous vectorfield, we define a new \mathbf Z₂-index and we construct a index theory for heteroclinic orbits of nonautonomous vectorfield. We prove an index theorem, by showing that, under some standard transversality assumptions, the \mathbf Z₂-index is equal to the parity, a homotopy invariant for paths of Fredholm operators of index 0. As a direct consequence of the index theory developed in this paper, we get a new bifurcation result for heteroclinic orbits.

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