- 00-35 P. Bernard
- Homoclinic orbit to a center manifold
Jan 22, 00
(auto. generated ps),
of related papers
Abstract. A fixed point of saddle-center type
of an autonomous Hamiltonian system
is contained in a local
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.