Below is the ascii version of the abstract for 04-123.
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Michele V. Bartuccelli, Alberto Berretti, Jonathan H.B. Deane, Guido Gentile, Stephen A. Gourley
Periodic orbits and scaling laws
for a driven damped quartic oscillator
ABSTRACT. In this paper we investigate the conditions under which periodic solutions
of a certain nonlinear oscillator persist when
the differential equation is perturbed by adding
a driving periodic force and a dissipative term.
We conjecture that for any periodic orbit,
characterized by its frequency, there exists a threshold
for the damping coefficient, above which the orbit disappears,
and that this threshold is infinitesimal in the perturbation parameter,
with integer order depending on the frequency.
Some rigorous analytical results toward the proof
of these conjectures are provided. Moreover the relative size
and shape of the basins of attraction of the existing
stable periodic orbits are investigated numerically,
giving further support to the validity of the conjectures.