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Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits. (English) Zbl 0787.34041
Homoclinic orbits for a time-periodic Hamiltonian system (*) z ˙=JH z (t,z), H=1 2Az,z+W(T,z) are found, assuming that z=0 is a hyperbolic equilibrium point and that W has global superquadratic growth in z. They are obtained as local C 1 - limits of certain nontrivial T-periodic solutions of (*) as T, where the hyperbolicity prevents them from shrinking to zero. This approach extends results by Rabinowitz for second order Hamiltonian systems, and it differs from corresponding results by Coti-Zelati, Ekeland & Séré and Hofer & Wysocki. The references are given in the paper.

MSC:
34C37Homoclinic and heteroclinic solutions of ODE