Información del autor
Autor Castrillón López, Marco |
Documentos disponibles escritos por este autor (60)
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The paper investigates an extension of Christoffel duality to a certain family of Sturmian words. Given an Christoffel prefix w of length N of an Sturmian word of slope g we associate a N-companion slope g(N)* such that the upper Sturmian word o[...]texto impreso
We show how to \concatenate" variational principles over different bases into one over a single base, thereby providing a unifed Lagrangian treatment of interacting systems. As an example we study a Klein Gordon feld interacting with a mesically[...]texto impreso
The goal of this short note is to show the geometric structure of the Euler-Poincaré reduction procedure in Field Theories with special emphasis on the nature of the set of variations and the set of admissible sections. The method of Lagrange mu[...]texto impreso
Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are,[...]texto impreso
We show how to enlarge the covariance groups of a wide variety of classical field theories in such a way that the resulting “covariantized” theories are éssentially equivalent to the originals. In particular, our technique will render many class[...]texto impreso
Let C be the bundle of connections of a principal G-bundle ?: P ? M,and let V be the vector bundle associated with P by a linear representation G ? GL(V ) on a finite-dimensional vector space V . The Lagrangians on J 1(C ×M V) whose current form[...]texto impreso
Guzmán Ozamiz, Miguel de ; Gaspar Alonso-Vega, María ; Castrillón López, Marco ; Soler Segura, Javier ; García Gual, Jesús Eduardo ; Hernández Gómez, Joaquín ; Sánchez García, Mercedes | Graó | 1999Este trabajo plantea con claridad un problemanteresante: la ausencia de un programa de detección, ayuda y estímulo para aquellos alumnos con capacidades matemáticas superiores a las habituales, muestra así mismo el retraso que esta situación den[...]texto impreso
The goal of this article is to give a simple formulation of some aspects about the construction of musical scales and the classical laws of consonance.texto impreso
Castrillón López, Marco ; Gadea, P.M. ; Muñoz Masqué, Jaime | the American Romanian Academy of Arts and Sciences (USA) | 1999The paper is a survey of several results by the authors, the main one of them being the following characterization of homogeneous algebraic distributions: Let us consider a vertical distribution D on the vector bundle p:E?M locally spanned by ve[...]texto impreso
Castrillón López, Marco ; Díaz-Cano Ocaña, Antonio ; Etayo Gordejuela, J. Javier ; Folgueira, Marta ; Infante del Río, Juan Antonio ; Pozo Coronado, Luis Miguel ; Rey Cabezas, Jose María | No publicado | 2013Material elaborado por profesores de la UCM para la asignatura de este nombre del grado en Ingeniería Matemáticas, el grado en Matemáticas y el grado en Matemáticas y Estadística. Contenidos: - Números enteros. Dígitos de control y criptografía[...]texto impreso
We compare Euler–Poincaré reduction in principal fibre bundles, as a constrained variational problem on the connections of this fibre bundle and constraint defined by the vanishing of the curvature of the connection, with the corresponding probl[...]texto impreso
Let G be a Lie group and let L:TG?R be a Lagrangian invariant under the natural action of G on its tangent bundle. Then L induces a function l:(TG)/G?g?R called the reduced Lagrangian, g being the Lie algebra of G. As is well known, the Euler-La[...]texto impreso
The goal of this short note is to show the constrained nature of the set of variations and the set of admissible sections of the Euler-Poincare reduction scheme for field theories in both the continuous formalism and in a discrete modeltexto impreso
El objetivo principal de esta memoria ha sido el estudio y caracterización de las formas gauge invariantes en el fibrado de las conexiones CP de un fibrado principal. Aprovechando la identificación entre CP y el cociente del fibrado de jets J1P [...]texto impreso
The classification of 4-dimensional naturally reductive pseudo-Riemannian spaces is given. This classification comprises symmetric spaces, the product of 3-dimensional naturally reductive spaces with the real line and new families of indecomposa[...]texto impreso
Let ?:P?M be a principal SU(2)-bundle, let autP [resp. gauP?autP] be the Lie algebra [resp. the ideal] of all G-invariant [resp. G-invariant ?-vertical] vector fields in X(P), and let p:C(P)?M be the bundle of connections of P. A differential fo[...]texto impreso
Let ?:P?M be a principal G-bundle. Then one can consider the following diagram of fibre bundles: \CD J^{1}(P) @> \pi_{10}> > P\\ @VqVV @VV\pi V\\ C(P) @> p> > M\endCD where p is the bundle of connections of ?. As is well known, q is also a pri[...]texto impreso
Given a principal bundle P?M we classify all first order Lagrangian densities on the bundle of connections associated to P that are invariant under the Lie algebra of infinitesimal automorphisms. These are shown to be variationally trivial and t[...]texto impreso
The structure of the algebra of gauge-invariant differential forms on the bundle C × ME is determined, where p:C?M is the bundle of connections of a U(1) principal bundle ? : P?M, and E?M is the associated bundle to P by the representation ?r, r[...]texto impreso
Let ?:P?M be a principal G-bundle. One denotes by J1P the 1-jet bundle of local sections of ?, by autP the Lie algebra of G-invariant vector fields of P and by gauP the ideal of ?-vertical vector fields in autP. A differential form ? on J1P is s[...]texto impreso
Let C ? M be the bundle of connections of a principal G-bundle P ? M over a pseudo-Riemannian manifold (M,g) of signature (n+, n?) and let E ? M be the associated bundle with P under a linear representation of G on a finite-dimensional vector sp[...]texto impreso
The paper presents some basic facts concerning the formulation of the gauge invariance property of the electromagnetic field in terms of differentiable manifolds. For example, the gauge potentials are identified as differential one-forms on the [...]texto impreso
One of the classical problems in the theory of variational calculus is the so-called equivalence problem, which studies whether two Lagrangians L, L?, defined in the 1-jet prolongation of a given bundle, determine the same variational problem. T[...]texto impreso
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Let C?M be the bundle of connections of a principal bundle on M . The solutions to Hamilton–Cartan equations for a gauge-invariant Lagrangian density ? on C satisfying a weak condition of regularity, are shown to admit an affine fibre-bundle [...]texto impreso
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Let p:E?M be a vector bundle of dimension n+m and (x?,yi), ?=1,…,n, i=1,…,m, be fibre coordinates. A vertical vector field X on E is said to be algebraic [respectively, algebraic homogeneous of degree d] if its coordinate expression is of the ty[...]texto impreso
Homogeneous Riemannian structures have been studied and classified in terms of tensors through the works of Ambrose-Singer and of Tricerri-Vanhecke, dating back to the 1950s and 1980s, respectively. More recently, an abstract representation theo[...]texto impreso
A classification of homogeneous quaternionic Kähler structures by real tensors is given and related to Fino’s representation theoretic decomposition. A relationship between the modules whose dimension grows linearly and quaternionic hyperbolic s[...]texto impreso
For each non-compact quaternion-Kähler symmetric space of dimension 8, all of its descriptions as a homogeneous Riemannian space (obtained through the Witte’s refined Langlands decomposition) and the associated homogeneous quaternionic Kähler st[...]texto impreso
The connected groups acting by isometries on either the real or the complex hyperbolic spaces are determined. A Lie-theoretic description of the homogeneous Riemannian, respectively Kähler, structures of linear type on these spaces is then found[...]texto impreso
It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing in the Lie algebra. Moreover, the Hamilton- Cartan equations of these Lagrangians are obtained and proved to be also [...]texto impreso
A principios del verano de este año, la Junta de Gobierno de la RSME ratificó la propuesta del jurado de la edición de 2011 del Premio José Luis Rubio de Francia de conceder dicho galardón a Alberto Enciso Carrasco. En la argumentación del jurad[...]texto impreso
Let M be a smooth oriented connected n-dimensional manifold and let M be the space of pseudo-Riemannian metrics on M of a given signature (n+,n?),n++n?=n> 1. A system of n metric invariants is attached to each metric in M, called the Ricci invar[...]texto impreso
Let P ? M be a principal G-bundle over a pseudo-Riemannian manifold (M, g). If G is semisimple, the Euler-Lagrange and the Hamilton-Cartan equations of the Yang-Mills Lagrangian defined by g are proved to remain unchanged if the Cartan-Killing m[...]texto impreso
This article studies generated scales having exactly three different step sizes within the language of algebraic combinatorics on words. These scales and their corresponding step-patterns are called non well formed. We prove that they can be nat[...]texto impreso
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Castrillón López, Marco ; Martín Peinador, Elena ; Rodríguez Sanjurjo, José Manuel ; Ruiz Sancho, Jesús María | Departamento de Geometría y Topología | 2015-09This volume contains the contributions presented by several colleagues as a tribute to the mathematical and human qualities of José María Montesinos Amilibia on the occasion of his seventieth birthday. The editors would like to express their tha[...]texto impreso
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This work is devoted to presenting a summary of results developed mainly by the first author, T. S. Ratiu and S. Shkoller in their previous work [Proc. Amer. Math. Soc. 128 (2000), no. 7, 2155–2164;]. The main results concern the reduction o[...]texto impreso
We give an exposition of the 1972 parametrization method of Kuchar in the context of the multisymplectic approach to field theory. The purpose of the formalism developed here is to make any classical field theory, containing a metric as a sole b[...]texto impreso
Castrillón López, Marco ; Valdés Morales, Antonio | 2001-05We show that projectively invariant evolution operators have unavoidable singularities. In particular, we see that there exists no non-singular projective evolution operator well-defined over straight lines nor conics.texto impreso
A general reduction theory for field theoretical Lagrangians on principal fiber bundles is presented. The reduced variational problem as well as the associated equations are formulated. The link between the solutions of the original problem and [...]texto impreso
Castrillón López, Marco ; Ratiu, Tudor S. ; Shkoller, Steve | American Mathematical Society | 1999-11-01In Lagrangian mechanics the simplest example of reduction is the Euler-Poincaré reduction. In this case, the configuration space is a Lie group G and the Lagrangian function L:TG?R is invariant under the natural action of the group on TG by righ[...]texto impreso
Basic results on gauge invariance of differential forms on the bundle of connections of an arbitrary principal U(1)-bundle and its associated bundles, are reviewed in terms of the underlying geometry to such bundles, within the framework of clas[...]texto impreso
This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian L or the momentum map J[...]