Now showing items 1-20 of 61

  • Action-angle variables and a KAM theorem for b-Poisson manifolds 

    Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey (2015-02)
    External research report
    Open Access
    In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we ...
  • Action-angle variables and a KAM theorem for b-Poisson manifolds 

    Miranda Galcerán, Eva; Kiesenhofer, Anna; Scott, Geoffrey (2016-01-01)
    Article
    Open Access
    In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle 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 Access
    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 ...
  • 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 Access
    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 ...
  • A normal form theorem for integrable systems on contact manifolds 

    Miranda Galcerán, Eva (2005)
    Article
    Open Access
    We 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 (2015-03)
    External research report
    Open Access
    In 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 b-manifolds 

    Miranda Galcerán, Eva; Martinez Torres, David; Frejlich, Pedro (2017)
    Article
    Open Access
    Poisson manifold (M2n; ) is b-symplectic if Vn is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address questions pertaining to b-symplectic manifolds. We pro- vide ...
  • A Poincaré lemma in geometric quantisation 

    Miranda Galcerán, Eva; Solha, Romero (American Institute of Mathematical Sciences, 2013-12)
    Article
    Open Access
    This 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^m-Nambu structures of top degree 

    Miranda Galcerán, Eva; Planas Bahí, Arnau (2018-01)
    Article
    Open Access
    We 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 Access
    In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending ...
  • Contact structures with singularities 

    Miranda Galcerán, Eva; Oms, Cédric (2018-06-15)
    External research report
    Open Access
    We 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 non-smooth differential ...
  • Convexity for Hamiltonian torus actions on b-symplectic manifolds 

    Guillemin, Victor; Miranda Galcerán, Eva; Pires, Ana Rita; Scott, Geoffrey (2017)
    Article
    Open Access
    n [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 ...
  • Convexity of the moment map image for torus actions on b(m)-symplectic manifolds 

    Miranda Galcerán, Eva; Guillemin, Victor; Weitsman, Jonathan (Royal Society, 2018-10-28)
    Article
    Open Access
    We prove a convexity theorem for the image of the moment map of a Hamiltonian torus action on a bm-symplectic 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 (2016-07)
    Article
    Open Access
    We associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on b-Poisson/b-symplectic manifolds. The semilocal equivalence with such models uses the corresponding ...
  • Coupling symmetries with Poisson structures 

    Laurent-Gengoux, Camille; Miranda Galcerán, Eva (2012-10-30)
    External research report
    Restricted access - author's decision
    In 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 policy
    We 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^m-symplectic structures 

    Miranda Galcerán, Eva; Guillemin, Victor; Weitsman, Jonathan (2017)
    Article
    Open Access
    A 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 ...
  • Equivariant classification of bm-symplectic surfaces 

    Miranda Galcerán, Eva; Planas Bahí, Arnau (Springer, 2018-07-24)
    Article
    Open Access
    Inspired 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 non-integrable systems on singular symplectic manifolds 

    Delshams Valdés, Amadeu; Miranda Galcerán, Eva; Kiesenhofer, Anna (2016-12)
    External research report
    Open Access
    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 ...
  • Examples of integrable and non-integrable systems on singular symplectic manifolds 

    Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Kiesenhoferb, Anna (2016)
    Article
    Open Access
    We 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 ...