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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 $(*)$ $\dot z =JH\sb z(t,z)$, $H={1 \over 2}\langle Az,z \rangle+W(T,z)$ 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 $C\sp 1$- limits of certain nontrivial $T$-periodic solutions of $(*)$ as $T \to \infty$, 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.

34C37Homoclinic and heteroclinic solutions of ODE
Full Text: DOI
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