 99365 Patrick BERNARD
 Homoclinic orbits in families of hypersurfaces with hyperbolic periodic
orbits.
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Sep 30, 99

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Abstract. We consider a Hamiltonian system in C^n having an invariant plane
with harmonic oscillations on it. We assume that this plane is
hyperbolic, which means that the oscillations are hyperbolic with
respect to their energy shell. We use variational theory to prove
that, under global hypothesis, many of these oscillations
have an homoclinic orbit, more precisely we prove that the periodic
orbits having an homoclinic are dense in the invariant plane
outside of a compact set. The major difficulty here is that the
periodic orbits are not hyperbolic with repect to the full phase space.
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