Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : A saddle-center fixed point of an autonomous Hamiltonian system is contained in a two-dimensional local invariant manifold, filled with periodic orbits and called the center manifold.Under certain hypotheses and when the center manifold is global, we prove the existence of an orbit homoclinic to one of the periodicorbits fillig the center manifold. In addition, we give explicit estimates which allow, in certain instances, to prove that the periodic orbit having an homoclinic orbit is close to the fixed point. As an exemple, we obtain the existence of an orbit homoclinic to one of the unstable oscillations of a sufficiently stiff elastic pendulum.
 
 
HOMOCLINIC ORBIT TO A CENTER MANIFOLD
BERNARD Patrick
2000-7
30-01-2000
 
Université de PARIS - DAUPHINE
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