Now showing items 1-16 of 16

• #### An application of functional analysis in a predator - prey system ﻿

(M. Sambandham, et al., 2005)
Conference report
Open Access
In this paper I want to show some advantages of the Geometric Iteration to a possible study of a predator-prey system. The Geometric Iteration presents characteristics such as continuity, derivability and integrability ...
• #### Darboux integrals for Schrödinger planar vector fields via Darboux transformations ﻿

(2012-07-14)
Article
Open Access
In this paper we study the Darboux transformations of planar vector fields of Schr odinger type. Using the isogaloisian property of Darboux transformation we prove the \invariance" of the objects of the \Darboux theory ...
• #### Darboux integrals for Schrödinger planar vector fields via Darboux transformations ﻿

(2011-11-01)
External research report
Open Access
In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the “invariance” of the elements of the “Darboux Theory of ...
• #### Galoisian approach to supersymmetric quantum mechanics ﻿

(Universitat Politècnica de Catalunya, 2009-07-02)
Doctoral thesis
Open Access
• #### Genealogía de permutaciones simples de orden una potencia de dos ﻿

(2006-02)
Article
Open Access
The aim of this paper is to show some properties of simple permutations with order a power of two and to give a combinatorial formula to determine its genealogy involving two new operations: the \textit{pasting} operation ...
• #### La teoría de Morales-Ramis y el algoritmo de Kovacic ﻿

(2006)
Working paper
Open Access
La teor\'\ı a de Morales–Ramis es la teor\'\ı a de Galois en el contexto de los sistemas din\'amicos y relaciona dos tipos diferentes de integrabilidad: integrabilidad en el sentido de Liouville de un sistema hamiltoniano e ...
• #### Non-autonomous hamiltonian systems and Morales-Ramis theory ﻿

(2008-06)
Article
Open Access
In this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with $1+1/2$ degree of ...
• #### Non-integrability of some few body problems in two degrees of freedom ﻿

(2008-11-16)
Article
Open Access
The basic theory of Differential Galois and in particular Morales--Ramis theory is reviewed with focus in analyzing the non--integrability of various problems of few bodies in Celestial Mechanics. The main theoretical ...
• #### Non-integrability of some hamiltonians with rational potentials ﻿

(2008-09-01)
Article
Open Access
In this paper we give a mechanism to compute the families of classical hamiltonians of two degrees of freedom with an invariant plane and normal variational equations of Hill-Schr\"odinger type selected in a suitable ...
• #### Notas del primer seminario de integrabilidad de la Universitat Politècnica de Catalunya ﻿

(Primitivo Belén Acosta Humánez, 2008)
Working paper
Open Access
Estas notas corresponden a las exposiciones presentadas en el \emph{Primer Seminario de Integrabilidad}, dentro de lo que se denomina \emph{Aula de Sistemas Din\'amicos}. Durante este evento se realizaron seis conferencias, ...
• #### On Hamiltonian potentials with cuartic polynomial normal variational equations ﻿

(2008-08)
Article
Open Access
Here we find the complete family of two degree of freedom classical Hamiltonians with invariant plane $\Gamma=\{q_2=p_2=0\}$ whose normal variational equation around integral curves in $\Gamma$ is a generically a ...
• #### On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory ﻿

(2012-01-12)
External research report
Open Access
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results ...
• #### On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory ﻿

(2015-05-01)
Article
Restricted access - publisher's policy
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results ...
• #### Teoremas de isomorfía en grupos diedros ﻿

(2003)
Working paper
Open Access
En este art\'\ı culo discutimos los resultados principales alcanzados en mi trabajo de grado, el cual fue dirigido por el profesor Jairo Charris Casta\~neda. La discusi\'on la limitaremos a los llamados $(p, q)$ grupos, ...
• #### Teoría de Galois diferencial: una aproximación ﻿

(2007)
Article
Open Access
En este artículo presentamos una descripción básica de la teoría de Galois diferencial, también conocida como teoría de Picard - Vessiot. Empezamos comparando la versión clásica de la teoría de Galois con la versión ...