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Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems
dc.contributor.author | Delshams Valdés, Amadeu |
dc.contributor.author | Huguet Casades, Gemma |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2008-12-12T18:06:20Z |
dc.date.available | 2008-12-12T18:06:20Z |
dc.date.issued | 2008-12-08 |
dc.identifier.uri | http://hdl.handle.net/2117/2438 |
dc.description.abstract | In the present paper we consider the case of a general $\cont{r+2}$ perturbation, for $r$ large enough, of an a priori unstable Hamiltonian system of $2+1/2$ degrees of freedom, and we provide explicit conditions on it, which turn out to be $\cont{2}$ generic and are verifiable in concrete examples, which guarantee the existence of Arnold diffusion. This is a generalization of the result in Delshams et al., \emph{Mem. Amer. Math. Soc.}, 2006, where it was considered the case of a perturbation with a finite number of harmonics in the angular variables. The method of proof is based on a careful analysis of the geography of resonances created by a generic perturbation and it contains a deep quantitative description of the invariant objects generated by the resonances therein. The scattering map is used as an essential tool to construct transition chains of objects of different topology. The combination of quantitative expressions for both the geography of resonances and the scattering map provides, in a natural way, explicit computable conditions for instability. |
dc.format.extent | 92 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
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 | Differentiable dynamical systems |
dc.subject.lcsh | Partial differential equations |
dc.subject.lcsh | Differential equations |
dc.subject.other | Arnold diffusion |
dc.subject.other | global instability |
dc.subject.other | KAM theory |
dc.subject.other | homoclinic and heteroclinic orbits |
dc.subject.other | Resonances |
dc.subject.other | Averaging method |
dc.subject.other | shadowing |
dc.title | Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems |
dc.type | Article |
dc.subject.lemac | Hamilton, Sistemes de |
dc.subject.lemac | Sistemes dinàmics diferenciables |
dc.subject.lemac | Equacions en derivades parcials |
dc.subject.lemac | Equacions diferencials ordinàries |
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::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
dc.subject.ams | Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions |
dc.subject.ams | Classificació AMS::34 Ordinary differential equations::34C Qualitative theory |
dc.rights.access | Open Access |
dc.relation.projectidctt | J-01135 |
local.personalitzacitacio | true |
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