Henk W. Broer, Heinz Hanßmann, Florian Wagener
Persistence Properties of Normally Hyperbolic Tori
(735K, PostScript)
ABSTRACT. Near-resonances between frequencies notoriously
lead to small denominators when trying to prove persistence
of invariant tori carrying quasi-periodic motion. In
dissipative systems external parameters detuning the
frequencies are needed so that Diophantine conditions
can be formulated, which allow to solve the homological
equation that yields a conjugacy between perturbed and
unperturbed quasi-periodic tori. The parameter values for
which the Diophantine conditions are not fulfilled form
the so-called resonance gaps. Normal hyperbolicity can
guarantee invariance of the perturbed tori, if not their
quasi-periodicity, for larger parameter ranges. For a
1-dimensional parameter space this allows to close almost
all resonance gaps.