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dc.contributor.authorDelshams Valdés, Amadeu
dc.contributor.authorMiranda Galcerán, Eva
dc.contributor.authorKiesenhofer, Anna
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationDelshams, A., Miranda, E., Kiesenhofer, A. "Examples of integrable and non-integrable systems on singular symplectic manifolds". 2016.
dc.description.abstractWe 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.extent14 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshSymplectic manifolds
dc.titleExamples of integrable and non-integrable systems on singular symplectic manifolds
dc.typeExternal research report
dc.subject.lemacTopologia algebraica
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.contributor.groupUniversitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.rights.accessOpen Access
upcommons.citation.authorDelshams, A., Miranda, E., Kiesenhofer, A.

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