Exploració per tema "Symplectic Geometry"
Ara es mostren els items 1-11 de 11
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An invitation to singular symplectic geometry
(2019)
Article
Accés obertIn 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 ... -
Bohr–Sommerfeld quantization of b-symplectic toric manifolds
(2023)
Article
Accés obertWe define the Bohr-Sommerfeld quantization via T -modules for a b-symplectic toric manifold and show that it coincides with the formal geometric quantization of [Victor W. Guillemin, Eva Miranda, and Jonathan Weitsman. On ... -
Convexity for Hamiltonian torus actions on b-symplectic manifolds
(2017)
Article
Accés obertn [GMPS] we proved that the moment map image of a b-symplectic toric manifold is a convex b-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on b-symplectic ... -
Desingularizing b^m-symplectic structures
(2015-12)
Report de recerca
Accés obertA 2n-dimensional Poisson manifold (M,¿) is said to be bm-symplectic if it is symplectic on the complement of a hypersurface Z and has a simple Darboux canonical form at points of Z which we will describe below. In this ... -
Geometric quantization via cotangent models
(2022-05-05)
Report de recerca
Accés obertIn this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the ... -
Integrable systems on singular symplectic manifolds: from local to global
(2021-02-03)
Report de recerca
Accés obertIn this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes ... -
Non-commutative integrable systems on b-symplectic manifolds
(2016)
Report de recerca
Accés obertIn this paper we study non-commutative integrable systems on b-Poisson manifolds. One important source of examples (and motiva- tion) of such systems comes from considering non-commutative systems on manifolds with ... -
On the singular Weinstein conjecture and the existence of escape orbits for b-Beltrami fields
(2021-10-07)
Report de recerca
Accés obertMotivated by Poincare’s orbits going to infinity in the (restricted) three-body problem ´ (see [29] and [7]), we investigate the generic existence of heteroclinic-like orbits in a neighbourhood of the critical set of a ... -
Open problems, questions, and challenges in finite-dimensional integrable systems
(2018-04-11)
Report de recerca
Accés obertThe paper surveys open problems and questions related to different aspects of integrable systems with finitely many degrees of freedom. Many of the open problems were suggested by the participants of the conference ... -
Symplectic and Poisson geometry on b-manifolds
(2012)
Report de recerca
Accés obertLet M2n be a Poisson manifold with Poisson bivector field . We say thatM is b-Poisson if the map n : M ! 2n(TM) intersects the zero section transversally on a codimension one submanifold Z M. This paper will be a ... -
Symplectic toric manifolds, Delzant theorem and integrable sytems
(Universitat Politècnica de Catalunya, 2017-07)
Treball Final de Grau
Accés obertEn aquesta tesi estudiarem la relació entre les varietats simplèctiques tòriques i els sistemes integrables. Per això, presentem en primer lloc tots els preliminars necessaris de geometria simplèctica. Després presentem ...