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Examples of integrable and non-integrable systems on singular symplectic manifolds
dc.contributor.author | Delshams Valdés, Amadeu |
dc.contributor.author | Miranda Galcerán, Eva |
dc.contributor.author | Kiesenhofer, Anna |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-04-05T09:58:51Z |
dc.date.available | 2016-04-05T09:58:51Z |
dc.date.issued | 2016-12 |
dc.identifier.citation | Delshams, A., Miranda, E., Kiesenhofer, A. "Examples of integrable and non-integrable systems on singular symplectic manifolds". 2016. |
dc.identifier.uri | http://hdl.handle.net/2117/85177 |
dc.description.abstract | We present a collection of examples borrowed from celes- tial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization trans- formations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lower- ing its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with sin- gularities which are mainly of two types: b m -symplectic and m -folded symplectic structures. These examples comprise the three body prob- lem as non-integrable exponent and some integrable reincarnations such as the two xed-center problem. Given that the geometrical and dy- namical properties of b m -symplectic manifolds and folded symplectic manifolds are well-understood [GMP, GMP2, GMPS, KMS, Ma, CGP, GL, GLPR, MO, S, GMW], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint. |
dc.format.extent | 14 p. |
dc.language.iso | eng |
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 | Symplectic manifolds |
dc.title | Examples of integrable and non-integrable systems on singular symplectic manifolds |
dc.type | External research report |
dc.subject.lemac | Topologia algebraica |
dc.contributor.group | Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC |
dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
dc.relation.publisherversion | http://arxiv.org/abs/1512.08293 |
dc.rights.access | Open Access |
local.identifier.drac | 17377027 |
dc.description.version | Preprint |
local.citation.author | Delshams, A.; Miranda, E.; Kiesenhofer, A. |
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