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dc.contributor.authorBroer, H. W.
dc.contributor.authorHanssmann, Heinz
dc.contributor.authorJorba, Angel
dc.contributor.authorVillanueva Castelltort, Jordi
dc.contributor.authorWagener, Florian
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2007-05-07T14:54:35Z
dc.date.available2007-05-07T14:54:35Z
dc.date.created2003
dc.date.issued2003
dc.identifier.urihttp://hdl.handle.net/2117/897
dc.description.abstractWe perform a bifurcation analysis of normal–internal resonances in parametrised families of quasi–periodically forced Hamiltonian oscillators, for small forcing. The unforced system is a one degree of freedom oscillator, called the ‘backbone’ system; forced, the system is a skew–product flow with a quasi–periodic driving with basic frequencies. The dynamics of the forced system are simplified by averaging over the orbits of a linearisation of the unforced system. The averaged system turns out to have the same structure as in the well–known case of periodic forcing ; for a real analytic system, the non–integrable part can even be made exponentially small in the forcing strength. We investigate the persistence and the bifurcations of quasi–periodic –dimensional tori in the averaged system, filling normal–internal resonance ‘gaps’ that had been excluded in previous analyses. However, these gaps cannot completely be filled up: secondary resonance gaps appear, to which the averaging analysis can be applied again. This phenomenon of ‘gaps within gaps’ makes the quasi–periodic case more complicated than the periodic case.
dc.format.extent36
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.subject.lcshHamiltonian dynamical systems
dc.subject.lcshLagrangian functions
dc.subject.lcshNonlinear Dynamics
dc.subject.lcshGlobal analysis (Mathematics)
dc.subject.lcshHamiltonian systems
dc.subject.lcshDifferential equations
dc.subject.otherquasi–periodically forced oscillators
dc.titleNormal-internal resonances in quasi-periodically forced oscillators: a conservative approach
dc.typeArticle
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacLagrange, Funcions de
dc.subject.lemacPartícules (Física nuclear)
dc.subject.lemacEquacions diferencials ordinàries
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34C Qualitative theory
dc.subject.amsClassificació AMS::58 Global analysis, analysis on manifolds::58K Theory of singularities and catastrophe theory
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics
dc.rights.accessOpen Access
local.personalitzacitaciotrue


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