Henk Broer, Heinz Hanßmann, Àngel Jorba, Jordi Villanueva, Florian Wagener
Quasi-Periodic Response Solutions at Normal-Internal Resonances
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ABSTRACT.  In the conservative dynamics of certain quasi-periodically
forced oscillators, normal-internal resonances are considered in a
bifurcational setting. The unforced system is a one degree of freedom
oscillator, under forcing the system becomes a skew-product flow with
a quasi-periodic motion on an $n$-dimensional torus as driving
system. In this work, we investigate the persistence and the
bifurcations of quasi-periodic $n$-dimensional tori (so-called
`response solutions') in the averaged system, filling normal-internal
resonance `gaps' that had been excluded in previous analyses.