03-392 Henk Broer, Heinz Hanßmann, Àngel Jorba, Jordi Villanueva, Florian Wagener

Quasi-Periodic Response Solutions at Normal-Internal Resonances (4137K, PostScript, gzipped and uuencoded) Aug 30, 03

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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.

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