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dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorGutiérrez Serrés, Pere
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.description.abstractWe 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.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshHamiltonian systems
dc.subject.lcshHamiltonian dynamical systems
dc.subject.lcshLagrangian functions
dc.subject.otherKAM theorem
dc.subject.otherelliptic equilibrium point
dc.titleExponentially small estimates for KAM theorem near an elliptic equilibrium point
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacLagrange, Funcions de
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::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.rights.accessOpen Access

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