Now showing items 1-12 of 12

  • Cotangent bundle reduction with singularities 

    Rodríguez Olmos, Miguel Andrés (2010)
    Lecture
    Open Access
  • Geometric properties of the scattering map of a normally hyperbolic invariant manifold 

    Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; Seara, Tere M. (2006-10-10)
    Article
    Open Access
    Given a normally hyperbolic invariant manifold $\Lambda$ for a map $f$, whose stable and unstable invariant manifolds intersect transversally, we consider its associated scattering map. That is, the map that, given an ...
  • Integrable Systems in singular symplectic manifolds 

    Cardona Aguilar, Robert (Universitat Politècnica de Catalunya, 2018-07)
    Master thesis
    Open Access
    En aquest treball es presenten les nocions de geometria simplèctica, de Poisson i b-simplèctica. En cada cas està demostrat un teorema de Arnold-Liouville per a sistemes integrables. Desprès de demostrar una part d'aquests ...
  • Lagrangian Lie subalgebroids of the canonical symplectic Lie algebroid 

    Aymerich Valls, Mónica (Universitat Politècnica de Catalunya, 2011-02)
    Master thesis
    Open Access
    It is well-known that the Poisson reduction of a hamiltonian system on the cotangent bundle of a manifold produces a hamiltonian system on a linear Poisson manifold. On the other hand, linear Poisson structures on a vector ...
  • Morse theory and Floer homology 

    Brugués Mora, Joaquim (Universitat Politècnica de Catalunya, 2019-01)
    Master thesis
    Open Access
    Morse homology studies the topology of smooth manifolds by examining the critical points of a real-valued function defined on the manifold, and connecting them with the negative gradient of the function. Rather surprisingly, ...
  • Multisymplectic unified formalism for Einstein-Hilbert gravity 

    Gaset Rifà, Jordi; Román Roy, Narciso (2018-03-01)
    Article
    Open Access
    We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of ...
  • Order reduction, projectability and constrainsts of second-order field theories and higuer-order mechanics 

    Gaset Rifà, Jordi; Román Roy, Narciso (2016-12-01)
    Article
    Open Access
    The consequences of the projectability of Poincar\'e-Cartan forms in a third-order jet bundle $J^3\pi$ to a lower-order jet bundle are analyzed using the constraint algorithm for the Euler-Lagrange equations in $J^3\pi$. ...
  • Remarks on multisymplectic reduction 

    Echeverría Enríquez, Arturo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2018-06-01)
    Article
    Restricted access - publisher's policy
    The problem of reduction of multisymplectic manifolds by the action of Lie groups is stated and discussed, as a previous step to give a fully covariant scheme of reduction for classical field theories with symmetries.
  • Rigidity of hamiltonian actions on poisson manifolds 

    Miranda Galcerán, Eva; Tien Zung, Nguyen; Monnier, Philippe (2012)
    Article
    Restricted access - publisher's policy
  • Symplectic structures with singularities 

    Planas Bahí, Arnau (Universitat Politècnica de Catalunya, 2015-10)
    Master thesis
    Open Access
    The main goal of the thesis is to classify some particular Poisson structures, called b-Poisson, following results of Guillemin-Miranda-Pirés and Radko. To understand these results, this thesis contains some chapters of ...
  • Symplectic toric manifolds, Delzant theorem and integrable sytems 

    Cardona Aguilar, Robert (Universitat Politècnica de Catalunya, 2017-07)
    Bachelor thesis
    Open Access
    En 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 ...
  • Variational principles and symmetries on fibered multisymplectic manifolds 

    Gaset Rifà, Jordi; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2016-12-01)
    Article
    Open Access
    The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multi-symplectic structure. Then, for the corresponding variational equations, conserved quantities ...