Ara es mostren els items 1-20 de 41

    • A b-symplectic slice theorem 

      Braddell, Roisin; Miranda Galcerán, Eva; Kiesenhofer, Anna (2022-08-03)
      Article
      Accés obert
      In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of -symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864–896, we prove ...
    • b-Structures on Lie groups and Poisson reduction 

      Miranda Galcerán, Eva; Kiesenhofer, Anna; Braddell, Roisin (2022-02-11)
      Article
      Accés obert
      Motivated by the group of Galilean transformations and the subgroup of Galilean transformations which fix time zero, we introduce the notion of a b-Lie group as a pair where G is a Lie group and H is a codimension-one Lie ...
    • Bohr-Sommerfeld quantization of b-symplectic toric manifolds 

      Miranda Galcerán, Eva; Mir Garcia, Pau; Weitsman, Jonathan (2022-03-07)
      Report de recerca
      Accés obert
      We 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 [GMW18b]. In particular, we prove that its dimension is given ...
    • Bohr–Sommerfeld quantization of b-symplectic toric manifolds 

      Mir Garcia, Pau; Miranda Galcerán, Eva; Weitsman, Jonathan (2023)
      Article
      Accés obert
      We 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 ...
    • Constrained Lagrangian dissipative contact dynamics 

      de León Rodríguez, Manuel; Lainz Valcázar, Manuel; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2021-12-28)
      Article
      Accés obert
      We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on a dissipative variable with an adequate ...
    • Constraint algorithm for singular field theories in the k-cosymplectic framework 

      Gràcia Sabaté, Francesc Xavier; Rivas Guijarro, Xavier; Román Roy, Narciso (American Institute of Mathematical Sciences, 2020-03-15)
      Article
      Accés obert
      The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of k-cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of ...
    • Cotangent bundle reduction with singularities 

      Rodríguez Olmos, Miguel Andrés (2010)
      Presentació
      Accés obert
    • Geometric Hamilton-Jacobi theory for higher-order autonomous systems 

      Colombo, Leonardo; De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2014-06-13)
      Article
      Accés restringit per política de l'editorial
      The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the background of higher-order mechanical systems, in both the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding ...
    • Geometric Hamilton-Jacobi theory for higher-order autonomous systems 

      Colombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2013-09-09)
      Report de recerca
      Accés obert
      The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding ...
    • Geometric quantization via cotangent models 

      Miranda Galcerán, Eva; Mir Garcia, Pau (2022-05-05)
      Report de recerca
      Accés obert
      In 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 ...
    • Geometric quantization via cotangent models 

      Mir Garcia, Pau; Miranda Galcerán, Eva (2021-09)
      Article
      Accés obert
      In 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 ...
    • Higher-order contact mechanics 

      De León, Manuel; Gaset Rifà, Jordi; Lainz Valcázar, Manuel; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (Elsevier, 2021-02-01)
      Article
      Accés obert
      We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent ...
    • Integrable Systems in singular symplectic manifolds 

      Cardona Aguilar, Robert (Universitat Politècnica de Catalunya, 2018-07)
      Projecte Final de Màster Oficial
      Accés obert
      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 ...
    • Integrable systems on singular symplectic manifolds: from local to global 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva (2021-09-22)
      Article
      Accés obert
      In 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 ...
    • Integrable systems on singular symplectic manifolds: from local to global 

      Miranda Galcerán, Eva; Cardona, Robert (2021-02-03)
      Report de recerca
      Accés obert
      In 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 ...
    • k-cosymplectic formalism in classical field theory: the Skinner–Rusk approach 

      Rey, Angel M.; Román Roy, Narciso; Salgado, Modesto (2006-02-14)
      Article
      Accés obert
      The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order field theories are reviewed and completed. In particular they are stated for singular almost-regular systems. After that, both formalisms are unified ...
    • Lagrangian Lie subalgebroids of the canonical symplectic Lie algebroid 

      Aymerich Valls, Mónica (Universitat Politècnica de Catalunya, 2011-02)
      Projecte Final de Màster Oficial
      Accés obert
      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 ...
    • Lie-algebroid formulation of k-cosymplectic classical field theories 

      Román Roy, Narciso; Salgado, Modesto; Vilariño, Silvia (2009)
      Comunicació de congrés
      Accés restringit per política de l'editorial
      The k-cosymplectic formalism is the generalization to field theories of the cosymplectic formalism, which is the geometric framework for describing non-autonomous dynamical systems. In [5], A. Weinstein introduced a new ...
    • More insights into symmetries in multisymplectic field theories 

      Guerra IV, Arnoldo; Román Roy, Narciso (2023-02-01)
      Article
      Accés obert
      This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in ...
    • Morse theory and Floer homology 

      Brugués Mora, Joaquim (Universitat Politècnica de Catalunya, 2019-01)
      Projecte Final de Màster Oficial
      Accés obert
      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, ...