Browsing by Author "Miranda Galcerán, Eva"

Actionangle variables and a KAM theorem for bPoisson manifolds
Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey (201502)
External research report
Open AccessIn this article we prove an actionangle theorem for bintegrable systems on bPoisson manifolds improving the actionangle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we ... 
Actionangle variables and a KAM theorem for bPoisson manifolds
Miranda Galcerán, Eva; Kiesenhofer, Anna; Scott, Geoffrey (20160101)
Article
Open AccessIn this article we prove an actionangle theorem for bintegrable systems on bPoisson manifolds improving the actionangle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we ... 
An invitation to singular symplectic geometry
Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Dempsey Bradell, Roisin Mary; Oms, Cedric; Planas Bahí, Arnau (2019)
Article
Open AccessIn this paper we analyze in detail a collection of motivating examples to consider bmsymplectic forms and foldedtype symplectic structures. In particular, we provide models in Celestial Mechanics for every bmsymplectic ... 
An invitation to singular symplectic geometry
Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Planas Bahí, Arnau; Oms, Cedric; Dempsey Bradell, Roisin Mary (2017)
External research report
Open AccessIn this paper we analyze in detail a collection of motivating examples to consider bm symplectic forms and foldedtype symplectic structures. In particular, we provide models in Celestial Mechanics for every bmsymplectic ... 
A normal form theorem for integrable systems on contact manifolds
Miranda Galcerán, Eva (2005)
Article
Open AccessWe present a normal form theorem for singular integrable systems on contact manifolds 
A note on symplectic and Poisson linearization of semisimple Lie algebra actions
Miranda Galcerán, Eva (201503)
External research report
Open AccessIn this note we prove that an analytic symplectic action of a semisimple Lie algebra can be locally linearized in Darboux coordinates. This result yields simultaneous analytic linearization for Hamiltonian vector fields ... 
A note on the symplectic topology of bmanifolds
Miranda Galcerán, Eva; Martinez Torres, David; Frejlich, Pedro (2017)
Article
Open AccessPoisson manifold (M2n; ) is bsymplectic if Vn is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address questions pertaining to bsymplectic manifolds. We pro vide ... 
A Poincaré lemma in geometric quantisation
Miranda Galcerán, Eva; Solha, Romero (American Institute of Mathematical Sciences, 201312)
Article
Open AccessThis article presents a Poincar e lemma for the Kostant complex, used to compute geometric quantisation, when the polarisation is given by a Lagrangian foliation de ned by an integrable system with nondegenerate singularities. 
Classification of b^mNambu structures of top degree
Miranda Galcerán, Eva; Planas Bahí, Arnau (201801)
Article
Open AccessWe obtain sufficient conditions for the existence and uniqueness of a positive compact almost automorphic solution to a logistic equation with discrete and continuous delay. Moreover, we provide a counterexample to some ... 
Codimension one symplectic foliations and regular Poisson manifolds
Guillemin, Victor; Miranda Galcerán, Eva; Pires, Ana Rita (2010)
External research report
Open AccessIn this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed oneform defining the symplectic foliation and a closed twoform extending ... 
Contact structures with singularities
Miranda Galcerán, Eva; Oms, Cédric (20180615)
External research report
Open AccessWe study singular contact structures, which are tangent to a given smooth hypersurface Z and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of nonsmooth differential ... 
Convexity for Hamiltonian torus actions on bsymplectic manifolds
Guillemin, Victor; Miranda Galcerán, Eva; Pires, Ana Rita; Scott, Geoffrey (2017)
Article
Open Accessn [GMPS] we proved that the moment map image of a bsymplectic toric manifold is a convex bpolytope. In this paper we obtain convexity results for the more general case of nontoric hamiltonian torus actions on bsymplectic ... 
Convexity of the moment map image for torus actions on b(m)symplectic manifolds
Miranda Galcerán, Eva; Guillemin, Victor; Weitsman, Jonathan (Royal Society, 20181028)
Article
Open AccessWe prove a convexity theorem for the image of the moment map of a Hamiltonian torus action on a bmsymplectic manifold. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods 
Cotangent models of integrable systems
Miranda Galcerán, Eva; Kiesenhofer, Anna (201607)
Article
Open AccessWe associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on bPoisson/bsymplectic manifolds. The semilocal equivalence with such models uses the corresponding ... 
Coupling symmetries with Poisson structures
LaurentGengoux, Camille; Miranda Galcerán, Eva (20121030)
External research report
Restricted access  author's decisionIn this paper we study normal forms problems for integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The ... 
Coupling symmetries with Poisson structures
Miranda Galcerán, Eva; Laurent Gengoux, Camille (Springer, 2013)
Article
Restricted access  publisher's policyWe study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of ... 
Desingularizing b^msymplectic structures
Miranda Galcerán, Eva; Guillemin, Victor; Weitsman, Jonathan (2017)
Article
Open AccessA 2ndimensional Poisson manifold (M; ) is said to be bmsymplectic 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 ... 
Equivariant classification of bmsymplectic surfaces
Miranda Galcerán, Eva; Planas Bahí, Arnau (Springer, 20180724)
Article
Open AccessInspired by Arnold’s classification of local Poisson structures [1] in the plane using the hierarchy of singularities of smooth functions, we consider the problem of global classification of Poisson structures on surfaces. ... 
Examples of integrable and nonintegrable systems on singular symplectic manifolds
Delshams Valdés, Amadeu; Miranda Galcerán, Eva; Kiesenhofer, Anna (201612)
External research report
Open AccessWe 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 ... 
Examples of integrable and nonintegrable systems on singular symplectic manifolds
Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Kiesenhoferb, Anna (2016)
Article
Open AccessWe present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell’s ...