Reports de recerca
http://hdl.handle.net/2117/85178
2017-11-22T17:06:10ZAn invitation to singular symplectic geometry
http://hdl.handle.net/2117/106301
An invitation to singular symplectic geometry
Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Planas Bahí, Arnau; Oms, Cedric; Dempsey Bradell, Roisin Mary
In this paper we analyze in detail a collection of motivating examples to consider bm-
symplectic forms and folded-type symplectic structures. In particular, we provide models in
Celestial Mechanics for every bm-symplectic structure. At the end of the paper, we introduce
the odd-dimensional analogue to b-symplectic manifolds: b-contact manifolds.
2017-07-10T09:18:33ZMiranda Galcerán, EvaDelshams Valdés, AmadeuPlanas Bahí, ArnauOms, CedricDempsey Bradell, Roisin MaryIn this paper we analyze in detail a collection of motivating examples to consider bm-
symplectic forms and folded-type symplectic structures. In particular, we provide models in
Celestial Mechanics for every bm-symplectic structure. At the end of the paper, we introduce
the odd-dimensional analogue to b-symplectic manifolds: b-contact manifolds.Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
http://hdl.handle.net/2117/85283
Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly-integrable
Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied.
2016-04-06T10:18:30ZDelshams Valdés, AmadeuGonchenko, MarinaGutiérrez Serrés, PereThe splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly-integrable
Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied.Examples of integrable and non-integrable systems on singular symplectic manifolds
http://hdl.handle.net/2117/85177
Examples of integrable and non-integrable systems on singular symplectic manifolds
Delshams Valdés, Amadeu; Miranda Galcerán, Eva; Kiesenhofer, Anna
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.
2016-04-05T09:58:51ZDelshams Valdés, AmadeuMiranda Galcerán, EvaKiesenhofer, AnnaWe 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.