Now showing items 1-18 of 18

(2010)
Lecture
Open Access
• #### Geometric Hamilton-Jacobi theory for higher-order autonomous systems ﻿

(2014-06-13)
Article
Restricted access - publisher's policy
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 ﻿

(2013-09-09)
External research report
Open Access
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 ...
• #### Integrable Systems in singular symplectic manifolds ﻿

(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 ...
• #### k-cosymplectic formalism in classical field theory: the Skinner–Rusk approach ﻿

(2006-02-14)
Article
Open Access
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 ﻿

(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 ...
• #### Lie-algebroid formulation of k-cosymplectic classical field theories ﻿

(2009)
Conference lecture
Restricted access - publisher's policy
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 ...
• #### Morse theory and Floer homology ﻿

(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 ﻿

(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 ...
• #### On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory ﻿

(2010-09-15)
External research report
Open Access
This 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 ...
• #### Order reduction, projectability and constrainsts of second-order field theories and higuer-order mechanics ﻿

(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 ﻿

(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 ﻿

(2012)
Article
Restricted access - publisher's policy
• #### Some topics concerning the theory of singular dynamical systems ﻿

(2006-03-01)
Article
Open Access
Some subjects related to the geometric theory of singular dynamical systems are reviewed in this paper. In particular, the following two matters are considered: the theory of canonical transformations for presymplectic ...
• #### Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory ﻿

(2007-03-12)
Article
Open Access
This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of ...
• #### Symplectic structures with singularities ﻿

(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 ﻿

(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 ﻿

(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 ...