dc.contributor.author Villanueva Castelltort, Jordi dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2016-11-09T08:12:30Z dc.date.available 2017-10-18T00:30:09Z dc.date.issued 2016-10-18 dc.identifier.citation Villanueva, J. A new approach to the parameterization method for Lagrangian tori of hamiltonian systems. "Journal of nonlinear science", 18 Octubre 2016, p. 1-36. dc.identifier.issn 0938-8974 dc.identifier.uri http://hdl.handle.net/2117/95852 dc.description.abstract We compute invariant Lagrangian tori of analytic Hamiltonian systems by the parameterization method. Under Kolmogorov’s non-degeneracy condition, we look for an invariant torus of the system carrying quasi-periodic motion with fixed frequencies. Our approach consists in replacing the invariance equation of the parameterization of the torus by three conditions which are altogether equivalent to invariance. We construct a quasi-Newton method by solving, approximately, the linearization of the functional equations defined by these three conditions around an approximate solution. Instead of dealing with the invariance error as a single source of error, we consider three different errors that take account of the Lagrangian character of the torus and the preservation of both energy and frequency. The condition of convergence reflects at which level contributes each of these errors to the total error of the parameterization. We do not require the system to be nearly integrable or to be written in action-angle variables. For nearly integrable Hamiltonians, the Lebesgue measure of the holes between invariant tori predicted by this parameterization result is of O(e1/2)O(e1/2) , where ee is the size of the perturbation. This estimate coincides with the one provided by the KAM theorem. dc.format.extent 36 p. dc.language.iso eng dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Hamiltonian systems dc.subject.lcsh Kolmogorov-Arnold-Moser theory dc.subject.other Hamiltonian systems dc.subject.other KAM theory dc.subject.other Lagrangian tori dc.subject.other Parameterization methods dc.title A new approach to the parameterization method for Lagrangian tori of hamiltonian systems dc.type Article dc.subject.lemac Sistemes hamiltonians dc.contributor.group Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC dc.identifier.doi 10.1007/s00332-016-9342-5 dc.description.peerreviewed Peer Reviewed dc.subject.ams Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems dc.subject.ams Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics dc.relation.publisherversion http://link.springer.com/article/10.1007%2Fs00332-016-9342-5 dc.rights.access Open Access drac.iddocument 19240583 dc.description.version Postprint (author's final draft) upcommons.citation.author Villanueva, J. upcommons.citation.published true upcommons.citation.publicationName Journal of nonlinear science upcommons.citation.startingPage 1 upcommons.citation.endingPage 36
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