Homotopy Classes for Stable Connections betweenHamiltonian Saddle-Focus

For a class of Hamiltonian systems in R 4 the set of homoclinic and hete-roclinic orbits which connect saddle-focus equilibria is studied using a vari-ational approach. The oscillatory properties of a saddle-focus equilibrium and the variational nature of the problem give rise to connections in many homotopy classes of the connguration plane punctured at the saddle-foci. This variational approach does not require any assumptions on the intersections of stable and unstable manifolds, such as transversality. Moreover, these connections are shown to be local minimizers of an associated action functional. This result has applications to spatial pattern formation in a class of fourth-order bistable evolution equations.

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