dc.contributor.author Delshams Valdés, Amadeu dc.contributor.author Gutiérrez Serrés, Pere dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I dc.date.accessioned 2007-05-09T15:48:27Z dc.date.available 2007-05-09T15:48:27Z dc.date.created 1997 dc.date.issued 1997 dc.identifier.uri http://hdl.handle.net/2117/963 dc.description.abstract We give a precise statement of KAM theorem for a Hamiltonian system in a neighborhood of an elliptic equilibrium point. If the frequencies of the elliptic point satisfy a Diophantine condition, with exponent $\tau$, and a nondegeneracy condition is fulfilled, we show that in a neighborhood of radius $r$ the measure of the complement of the KAM tori is exponentially small in $(1/r)^{1/(\tau+1)}$. This result is obtained by putting the system in Birkhoff normal form up to an appropriate order, and the key point relies on giving accurate estimates for its terms. dc.format.extent 5 dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 2.5 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/2.5/es/ dc.subject.lcsh Hamiltonian systems dc.subject.lcsh Hamiltonian dynamical systems dc.subject.lcsh Lagrangian functions dc.subject.other KAM theorem dc.subject.other elliptic equilibrium point dc.title Exponentially small estimates for KAM theorem near an elliptic equilibrium point dc.type Article dc.subject.lemac Hamilton, Sistemes de dc.subject.lemac Lagrange, Funcions de dc.contributor.group Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions 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::70H Hamiltonian and Lagrangian mechanics dc.rights.access Open Access
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