Quasi-periodic response solutions at normal-internal resonances

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 ``resonse solutions'') in the averaged system, filling normal-internal resonance `gaps' that had been excluded in previous analyses.