Now showing items 1-20 of 83

    • 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.
    • A Poincaré lemma in geometric quantisation 

      Miranda Galcerán, Eva; Solha, Romero (2013)
      External research report
      Open Access
      This paper presents a Poincaré lemma for the Kostant comple x, used to compute geometric quantisation, when the polarisat ion is given by a Lagrangian foliation defined by an integrable system wit h non-degenerate singularities.
    • 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 ...
    • 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 ...
    • 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 ...
    • b-Structures on Lie groups and Poisson reduction 

      Dempsey Bradell, Roisin Mary; Kiesenhofer, Anna; Miranda Galcerán, Eva (2020-09)
      External research report
      Open Access
      We introduce the notion of b-Lie group as a pair(G, H) where Gis a Lie group and H is a codimension-one Lie subgroup, and study the associated canonical b-symplectic structure on the b-cotangent bundle bT*G together with ...
    • Buscando órbitas períodicas 

      Miranda Galcerán, Eva (Real Sociedad Matemática Española, 2020-11-07)
      Article
      Open Access
      En este artículo presentamos una aproximación topológica y geométrica al estudio de órbitas periódicas (existencia y localización) tomando como punto de partida problemas de mecánica celeste. Describimos, a grandes rasgos, ...
    • 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 for Hamiltonian torus actions on b-symplectic manifolds 

      Guillemin, Victor; Miranda Galcerán, Eva; Pires, Ana Rita; Scott, Geoffrey (2014-12)
      External research report
      Open Access
      In [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 for integrable systems on $b$-symplectic manifolds 

      Miranda Galcerán, Eva; Kiesenhofer, Anna (2016-01)
      External research report
      Open Access
    • 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 

      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 ...