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Títol: A KAM theorem without action-angle variables for elliptic lower dimensional tori
Autor: Luque Jiménez, Alejandro
Villanueva Castelltort, Jordi
Altres autors/autores: Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
Matèries: Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
Hamiltonian systems
Elliptic invariant tori KAM theory Parameterization methods
Hamilton, Sistemes de
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Tipus de document: External research report
Descripció: We study elliptic lower dimensional invariant tori of Hamiltonian systems via parameterizations. The method is based in solving iteratively the functional equations that stand for invariance and reducibility. In contrast with classical methods, we do not assume that the system is close to integrable nor that is written in action-angle variables. We only require an approximation of an invariant torus of fixed vector of basic frequencies and a basis along the torus that approximately reduces the normal variational equations to constant coefficients. We want to highlight that this approach presents many advantages compared with methods which are built in terms of canonical transformations, e.g., it produces simpler and more constructive proofs that lead to more efficient numerical algorithms for the computation of these objects. Such numerical algorithms are suitable to be adapted in order to perform computer ssisted proofs.
Altres identificadors i accés: http://hdl.handle.net/2117/7067
Disponible al dipòsit:E-prints UPC
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