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Quasi-periodic response solutions at normal-internal resonances
Broer, H. W.; Hanssmann, Heinz; Jorba, Angel; Villanueva Castelltort, Jordi; Wagener, Florian
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Differential equations
Hamiltonian systems
Nonlinear Dynamics
Quasi-periodic response solutions
normal-internal resonances
Equacions diferencials ordinàries
Hamilton, Sistemes de
Partícules (Física nuclear)
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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