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Transversality of homoclinic orbits to hyperbolic 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 | 2012-12-10T11:45:28Z |
dc.date.available | 2012-12-10T11:45:28Z |
dc.date.created | 2012-07 |
dc.date.issued | 2012-07 |
dc.identifier.citation | Delshams, A.; Gutierrez, P.; Pacha, J. "Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation". 2012. |
dc.identifier.uri | http://hdl.handle.net/2117/17084 |
dc.description.abstract | The key point of our approach is to write the invariant manifolds in terms of generating functions, which are solutions of the Hamilton-Jacobi equation. In some examples, we show that it is enough to analyse the phase portrait of the Riccati equation without solving it explicitly. Finally, we consider an analogous problem in a perturbative situation. If the invariant manifolds of the unperturbed loop coincide, we have a problem of splitting of separatrices. In this case, the Riccati equation is replaced by a Mel0nikov potential defined as an integral, providing a condition for the existence of a perturbed loop and its transversality. This is also illustrated with a concrete example. |
dc.format.extent | 38 p. |
dc.language.iso | eng |
dc.relation.ispartofseries | [prepr201202DelGP] |
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.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 | Melnikov integr |
dc.title | Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation |
dc.type | External research report |
dc.subject.lemac | Sistemes dinàmics diferenciables |
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.relation.publisherversion | http://www.ma1.upc.edu/recerca/preprints/preprints-2012/Fitxers/prepr201201gutierrez.pdf |
dc.rights.access | Open Access |
local.identifier.drac | 10738606 |
dc.description.version | Preprint |
local.citation.author | Delshams, A.; Gutierrez, P.; Pacha, J. |
local.citation.publicationName | Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation |
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