TITLE:
Quasi-periodic response solutions at normal-internal resonances

AUTHORS:
Henk Broer^(1), Heinz Hanssmann^(2), Angel Jorba^(3),
Jordi Villanueva^(4), Florian Wagener^(5)

(1) broer@math.rug.nl
Instituut voor Wiskunde en Informatica (IWI), 
Rijksuniversiteit Groningen, 
Postbus 800, 9700 AV Groningen, The Netherlands.

(2) Heinz@iram.rwth-aachen.de
Institut fur Reine und Angewandte Mathematik der RWTH Aachen,
52056 Aachen, Germany.

(3) angel@maia.ub.es
Departament de Matematica Aplicada i Analisi,
Universitat de Barcelona,
Gran Via 585, 08007 Barcelona, Spain.

(4) jordi@vilma.upc.es
Departament de Matematica Aplicada I,
Universitat Politecnica de Catalunya,
Diagonal 647, 08028 Barcelona, Spain.

(5) f.o.o.wagener@uva.nl
Center for Nonlinear Dynamics in Economics and Finance (CeNDEF),
Department of Quantitative Economics, 
Universiteit van Amsterdam,
Roetersstraat 11, 
1018 WB Amsterdam, The Netherlands.

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.

This is a summary of a talk at the Equadiff meeting held in Hasselt,
Belgium, July 22-26, 2003.
