Mostra el registre d'ítem simple

dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorLlave Canosa, Rafael de la
dc.contributor.authorMartínez-Seara Alonso, M. Teresa
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2007-10-01T16:35:30Z
dc.date.available2007-10-01T16:35:30Z
dc.date.issued2003
dc.identifier.urihttp://hdl.handle.net/2117/1204
dc.description.abstractWe show that certain mechanical systems, including a geodesic °ow in any dimension plus a quasi-periodic perturbation by a potential, have orbits of unbounded energy. The assumptions we make in the case of geodesic °ows are: a) The metric and the external perturbation are smooth enough. b) The geodesic °ow has a hyperbolic periodic orbit such that its stable and unstable manifolds have a tranverse homoclinic intersection. c) The frequency of the external perturbation is Diophantine. d) The external potential satisØes a generic condition depending on the periodic orbit considered in b). The assumptions on the metric are C2 open and are known to be dense on many manifolds. The assumptions on the potential fail only in inØnite codimension spaces of potentials. The proof is based on geometric considerations of invariant manifolds and their intersections. The main tools include the scattering map of normally hyperbolic invariant manifolds, as well as standard perturbation theories (averaging, KAM and Melnikov techniques). We do not need to assume that the metric is Riemannian and we obtain results for Finsler or Lorentz metrics. Indeed, there is a formulation for Hamiltonian systems satisfying scaling hypotheses. We do not need to make assumptions on the global topology of the manifold nor on its dimension.
dc.format.extent97 pages
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.subject.lcshHamiltonian dynamical systems
dc.subject.lcshLagrangian functions
dc.subject.lcshDifferential geometry
dc.subject.lcshHamiltonian systems
dc.subject.lcshDifferentiable dynamical systems
dc.subject.otherorbits
dc.subject.otherquasi-periodic perturbations
dc.titleOrbits of unbounded energy in quasi-periodic perturbations of geodesic flows
dc.typeArticle
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacLagrange, Funcions de
dc.subject.lemacGeometria diferencial
dc.subject.lemacSistemes dinàmics diferenciables
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::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
dc.subject.amsClassificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.rights.accessOpen Access
local.personalitzacitaciotrue


Fitxers d'aquest items

Thumbnail

Aquest ítem apareix a les col·leccions següents

Mostra el registre d'ítem simple