00-35 P. Bernard

Homoclinic orbit to a center manifold (396K, postsript) Jan 22, 00

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Abstract. A fixed point of saddle-center type of an autonomous Hamiltonian system is contained in a local two-dimensional invariant manifold filled with periodic orbits and called the center manifold. We prove the existence of an orbit homoclinic to one of the periodic orbits filling the center manifold when this manifold is global, and under certain hypotheses. We moreover give estimates on its energy, which allow in certain instances to prove that the asymptotic periodic orbit is close to the fixed point. There are physical applications. For example we prove the existence of an orbit homoclinic to one of the unstable oscillations of a pendulum with a stiff elastic bar.

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