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Transversality of homoclinic orbits to hyberbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation
dc.contributor.author | Delshams Valdés, Amadeu |
dc.contributor.author | Gutiérrez Serrés, Pere |
dc.contributor.author | Pacha Andújar, Juan Ramón |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2011-12-27T11:21:16Z |
dc.date.available | 2011-12-27T11:21:16Z |
dc.date.created | 2011 |
dc.date.issued | 2011 |
dc.identifier.citation | Delshams, A.; Gutiérrez, P.; Pacha, J. "Transversality of homoclinic orbits to hyberbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation". 2011. |
dc.identifier.uri | http://hdl.handle.net/2117/14324 |
dc.description.abstract | We 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.extent | 35 p. |
dc.language.iso | eng |
dc.relation.ispartofseries | [prepr201111DelGP] |
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 | Differential equations |
dc.subject.other | transverse homoclinic orbits |
dc.subject.other | hyperbolic equilibria |
dc.subject.other | Hamilton{Jacobi equation |
dc.subject.other | Riccati equations |
dc.subject.other | splitting of separatrices |
dc.subject.other | Mel0nikov integrals |
dc.title | Transversality of homoclinic orbits to hyberbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation |
dc.type | External research report |
dc.subject.lemac | Equacions diferencials |
dc.subject.lemac | Hamilton, Sistemes de |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.relation.publisherversion | http://www.ma1.upc.edu/recerca/preprints2011.html |
dc.rights.access | Open Access |
local.identifier.drac | 8830548 |
dc.description.version | Preprint |
local.citation.author | Delshams, A.; Gutiérrez, P.; Pacha, J. |
local.citation.publicationName | Transversality of homoclinic orbits to hyberbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation |
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