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dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorGutiérrez Serrés, Pere
dc.contributor.authorPacha Andújar, Juan Ramón
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2011-12-27T11:21:16Z
dc.date.available2011-12-27T11:21:16Z
dc.date.created2011
dc.date.issued2011
dc.identifier.citationDelshams, A.; Gutiérrez, P.; Pacha, J. "Transversality of homoclinic orbits to hyberbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation". 2011.
dc.identifier.urihttp://hdl.handle.net/2117/14324
dc.description.abstractWe consider a Hamiltonian system with 2 degrees of freedom, with a hyperbolic equilibrium point having a loop or homoclinic orbit (or, alternatively, two hyperbolic equilibrium points connected by a heteroclinic orbit), as a step towards understanding the behavior of nearly-integrable Hamiltonians near double resonances. We provide a constructive approach to study whether the unstable and stable invariant manifolds of the hyperbolic point intersect transversely along the loop, inside their common energy level. For the system considered, we establish a necessary and suffcient condition for the transversality, in terms of a Riccati equation whose solutions give the slope of the invariant manifolds in a direction transverse to the loop.
dc.format.extent35 p.
dc.language.isoeng
dc.relation.ispartofseries[prepr201111DelGP]
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshDifferential equations
dc.subject.othertransverse homoclinic orbits
dc.subject.otherhyperbolic equilibria
dc.subject.otherHamilton{Jacobi equation
dc.subject.otherRiccati equations
dc.subject.othersplitting of separatrices
dc.subject.otherMel0nikov integrals
dc.titleTransversality of homoclinic orbits to hyberbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation
dc.typeExternal research report
dc.subject.lemacEquacions diferencials
dc.subject.lemacHamilton, Sistemes de
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.relation.publisherversionhttp://www.ma1.upc.edu/recerca/preprints2011.html
dc.rights.accessOpen Access
local.identifier.drac8830548
dc.description.versionPreprint
local.citation.authorDelshams, A.; Gutiérrez, P.; Pacha, J.
local.citation.publicationNameTransversality of homoclinic orbits to hyberbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation


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