Exploració per tema "Symplectic geometry"
Ara es mostren els items 8-27 de 41
-
Geometric Hamilton-Jacobi theory for higher-order autonomous systems
(2014-06-13)
Article
Accés restringit per política de l'editorialThe 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
(2013-09-09)
Report de recerca
Accés obertThe 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
(2022-05-05)
Report de recerca
Accés obertIn 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
(2021-09)
Article
Accés obertIn 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
(Elsevier, 2021-02-01)
Article
Accés obertWe 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
(Universitat Politècnica de Catalunya, 2018-07)
Projecte Final de Màster Oficial
Accés obertEn 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
(2021-09-22)
Article
Accés obertIn 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
(2021-02-03)
Report de recerca
Accés obertIn 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
(2006-02-14)
Article
Accés obertThe 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
(Universitat Politècnica de Catalunya, 2011-02)
Projecte Final de Màster Oficial
Accés obertIt 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
(2009)
Comunicació de congrés
Accés restringit per política de l'editorialThe 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
(2023-02-01)
Article
Accés obertThis 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
(Universitat Politècnica de Catalunya, 2019-01)
Projecte Final de Màster Oficial
Accés obertMorse 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, ... -
Multicontact formulation for non-conservative field theories
(Institute of Physics (IOP), 2023-01-13)
Article
Accés obertA new geometric structure inspired by multisymplectic and contact geometries, which we call multicontact structure, is developed to describe non-conservative classical field theories. Using the differential forms that ... -
Multisymplectic unified formalism for Einstein-Hilbert gravity
(2018-03-01)
Article
Accés obertWe 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 ... -
New multisymplectic approach to the Metric-Affine (Einstein-Palatini) action for gravity
(American Institute of Mathematical Sciences, 2019-09-01)
Article
Accés obertWe present a covariant multisymplectic formulation for the Einstein-Palatini (or Metric-Affine) model of General Relativity (without energy-matter sources). As it is described by a first-order affine Lagrangian (in the ... -
On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
(2010-09-15)
Report de recerca
Accés obertThis paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of ... -
On the singular Weinstein conjecture and the existence of escape orbits for b-Beltrami fields
(2021-10-07)
Report de recerca
Accés obertMotivated by Poincare’s orbits going to infinity in the (restricted) three-body problem ´ (see [29] and [7]), we investigate the generic existence of heteroclinic-like orbits in a neighbourhood of the critical set of a ... -
Order reduction, projectability and constrainsts of second-order field theories and higuer-order mechanics
(2016-12-01)
Article
Accés obertThe 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
(2018-06-01)
Article
Accés obertThe 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.