Departament de Matemàtiques
http://hdl.handle.net/2117/3917
2017-02-25T02:12:16ZThe group inverse of subdivision networks
http://hdl.handle.net/2117/101529
The group inverse of subdivision networks
Carmona Mejías, Ángeles; Mitjana Riera, Margarida; Monsó Burgués, Enrique P.J.
In this paper, given a network and a subdivision of it, we show how the Group Inverse of the subdivision network can be related to the Group Inverse of initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both networks and takes advantatge on the definition of the Group Inverse matrix.
2017-02-24T11:50:56ZCarmona Mejías, ÁngelesMitjana Riera, MargaridaMonsó Burgués, Enrique P.J.In this paper, given a network and a subdivision of it, we show how the Group Inverse of the subdivision network can be related to the Group Inverse of initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both networks and takes advantatge on the definition of the Group Inverse matrix.Functions and differentials on the non-split Cartan modular curve of level 11
http://hdl.handle.net/2117/101523
Functions and differentials on the non-split Cartan modular curve of level 11
Fernández González, Julio; González Rovira, Josep
The genus 4 modular curve Xns(11) attached to a non-split Cartan group of level 11
admits a model defined over Q. We compute generators for its function field in terms of
Siegel modular functions. We also show that its Jacobian is isomorphic over Q to the new
part of the Jacobian of the classical modular curve X0(121)
2017-02-24T10:48:02ZFernández González, JulioGonzález Rovira, JosepThe genus 4 modular curve Xns(11) attached to a non-split Cartan group of level 11
admits a model defined over Q. We compute generators for its function field in terms of
Siegel modular functions. We also show that its Jacobian is isomorphic over Q to the new
part of the Jacobian of the classical modular curve X0(121)Rigidity of infinitesimal momentum maps
http://hdl.handle.net/2117/101515
Rigidity of infinitesimal momentum maps
Miranda Galcerán, Eva; Esposito, Chiara
In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, this yields rigidity also for lifted actions to the symplectic groupoid.
2017-02-24T10:05:57ZMiranda Galcerán, EvaEsposito, ChiaraIn this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, this yields rigidity also for lifted actions to the symplectic groupoid.Redes estrella con la M-propiedad
http://hdl.handle.net/2117/101462
Redes estrella con la M-propiedad
Encinas Bachiller, Andrés Marcos
En este trabajo hacemos una aportación al problema inverso de M –matrices irreducibles, simétricas y singulares, que consiste en determinar c uándo su inversa de grupo es también una M –matriz. Mostramos primero que las matrices involucradas son las asociadas a operadores de Schr ¨odinger sobre redes cuyo pot encial está determinado por un peso sobre el conjunto de vértices. Particularizamos el a nálisis al caso de redes cuyo grafo subyacente es una estrella y mostramos que existen infi nitos operadores de Schr ¨odinger sobre ellas que satisfacen la propiedad descrita
2017-02-23T12:36:13ZEncinas Bachiller, Andrés MarcosEn este trabajo hacemos una aportación al problema inverso de M –matrices irreducibles, simétricas y singulares, que consiste en determinar c uándo su inversa de grupo es también una M –matriz. Mostramos primero que las matrices involucradas son las asociadas a operadores de Schr ¨odinger sobre redes cuyo pot encial está determinado por un peso sobre el conjunto de vértices. Particularizamos el a nálisis al caso de redes cuyo grafo subyacente es una estrella y mostramos que existen infi nitos operadores de Schr ¨odinger sobre ellas que satisfacen la propiedad descritaMultiplier ideals in two-dimensional local rings with rational singularities
http://hdl.handle.net/2117/101436
Multiplier ideals in two-dimensional local rings with rational singularities
Alberich Carramiñana, Maria; Álvarez Montaner, Josep; Dachs Cadefau, Ferran
The aim of this paper is to study jumping numbers and multiplier ideals of any ideal in a two-dimensional local ring with a rational singularity. In particular we reveal which information encoded in a multiplier ideal determines the next jumping number. This leads to an algorithm to compute sequentially the jumping numbers and the whole chain of multiplier ideals in any desired range. As a consequence of our method we develop the notion of jumping divisor that allows to describe the jump between two consecutive multiplier ideals. In particular we find a unique minimal jumping divisor that is studied extensively.
2017-02-23T09:19:50ZAlberich Carramiñana, MariaÁlvarez Montaner, JosepDachs Cadefau, FerranThe aim of this paper is to study jumping numbers and multiplier ideals of any ideal in a two-dimensional local ring with a rational singularity. In particular we reveal which information encoded in a multiplier ideal determines the next jumping number. This leads to an algorithm to compute sequentially the jumping numbers and the whole chain of multiplier ideals in any desired range. As a consequence of our method we develop the notion of jumping divisor that allows to describe the jump between two consecutive multiplier ideals. In particular we find a unique minimal jumping divisor that is studied extensively.Dynamics in the centre manifold around equilibrium points in periodically perturbed three-body problems
http://hdl.handle.net/2117/101316
Dynamics in the centre manifold around equilibrium points in periodically perturbed three-body problems
Le Bihan, Bastien; Masdemont Soler, Josep; Gomez Muntané, Gerard; Lizy-Destrez, Stephanie
A new application of the parameterization method is pre- sented to compute invariant manifolds about the equilib- rium points of Periodically Perturbed Three-Body Problems ( PPTBP ). These techniques are applied to obtain high-order semi-numerical approximations of the center manifolds abo ut the points L 1 , 2 of the Sun-perturbed Earth-Moon Quasi- Bicicular Problem ( QBCP ), which is a particular case of PPTBP . The quality of these approximations is compared with results obtained using equivalents of previous normal form procedures. Then, the parameterization is used to ini- tialize the computation of Poincaré maps, which allow to get a qualitative description of the periodically-perturb ed dynamics near the equilibrium points
2017-02-21T12:51:32ZLe Bihan, BastienMasdemont Soler, JosepGomez Muntané, GerardLizy-Destrez, StephanieA new application of the parameterization method is pre- sented to compute invariant manifolds about the equilib- rium points of Periodically Perturbed Three-Body Problems ( PPTBP ). These techniques are applied to obtain high-order semi-numerical approximations of the center manifolds abo ut the points L 1 , 2 of the Sun-perturbed Earth-Moon Quasi- Bicicular Problem ( QBCP ), which is a particular case of PPTBP . The quality of these approximations is compared with results obtained using equivalents of previous normal form procedures. Then, the parameterization is used to ini- tialize the computation of Poincaré maps, which allow to get a qualitative description of the periodically-perturb ed dynamics near the equilibrium pointsA continuous-time delay chaotic system obtained from a chaotic logistic map
http://hdl.handle.net/2117/101290
A continuous-time delay chaotic system obtained from a chaotic logistic map
Acho Zuppa, Leonardo
This paper presents a procedure to transform a chaotic logistic map into a continuous-time delay chaotic system by using sampled-data representation of continuous-time models. Because of this, the chaotic behavior of the resultant scheme is easy to proofread. A numerical illustration is also realized by utilizing Matlab/Simulink, where the new resultant chaotic attractor is shown
2017-02-21T10:56:40ZAcho Zuppa, LeonardoThis paper presents a procedure to transform a chaotic logistic map into a continuous-time delay chaotic system by using sampled-data representation of continuous-time models. Because of this, the chaotic behavior of the resultant scheme is easy to proofread. A numerical illustration is also realized by utilizing Matlab/Simulink, where the new resultant chaotic attractor is shownLa resolución numérica de ecuaciones de Viète y su difusión en el curso matemático de Hérigone
http://hdl.handle.net/2117/101287
La resolución numérica de ecuaciones de Viète y su difusión en el curso matemático de Hérigone
Massa Esteve, Maria Rosa; Linero Bas, Antonio
2017-02-21T10:36:54ZMassa Esteve, Maria RosaLinero Bas, AntonioLyubeznik numbers of local rings and linear strands of graded ideals
http://hdl.handle.net/2117/101277
Lyubeznik numbers of local rings and linear strands of graded ideals
Álvarez Montaner, Josep
We report recent work on the study of Lyubeznik numbers and their relation to invariants coming from the study of linear strands of free resolutions.
2017-02-21T09:43:13ZÁlvarez Montaner, JosepWe report recent work on the study of Lyubeznik numbers and their relation to invariants coming from the study of linear strands of free resolutions.Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument
http://hdl.handle.net/2117/101125
Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument
Delshams Valdés, Amadeu; Gidea, Marian; Roldán, Pablo
We consider the spatial circular restricted three-body problem, on the motion of an infinitesimal body under the gravity of Sun and Earth. This can be described by a 3-degree of freedom Hamiltonian system. We fix an energy level close to that of the collinear libration point L1, located between Sun and Earth. Near L1 there exists a normally hyperbolic invariant manifold, diffeomorphic to a 3-sphere. For an orbit confined to this 3-sphere, the amplitude of the motion relative to the ecliptic (the plane of the orbits of Sun and Earth) can vary only slightly.
We show that we can obtain new orbits whose amplitude of motion relative to the ecliptic changes significantly, by following orbits of the flow restricted to the 3-sphere alternatively with homoclinic orbits that turn around the Earth. We provide an abstract theorem for the existence of such ‘diffusing’ orbits, and numerical evidence that the premises of the theorem are satisfied in the three-body problem considered here. We provide an explicit construction of diffusing orbits.
The geometric mechanism underlying this construction is reminiscent of the Arnold diffusion problem for Hamiltonian systems. Our argument, however, does not involve transition chains of tori as in the classical example of Arnold. We exploit mostly the ‘outer dynamics’ along homoclinic orbits, and use very little information on the ‘inner dynamics’ restricted to the 3-sphere.
As a possible application to astrodynamics, diffusing orbits as above can be used to design low cost maneuvers to change the inclination of an orbit of a satellite near L1 from a nearly-planar orbit to a tilted orbit with respect to the ecliptic. We explore different energy levels, and estimate the largest orbital inclination that can be achieved through our construction.
2017-02-16T09:57:15ZDelshams Valdés, AmadeuGidea, MarianRoldán, PabloWe consider the spatial circular restricted three-body problem, on the motion of an infinitesimal body under the gravity of Sun and Earth. This can be described by a 3-degree of freedom Hamiltonian system. We fix an energy level close to that of the collinear libration point L1, located between Sun and Earth. Near L1 there exists a normally hyperbolic invariant manifold, diffeomorphic to a 3-sphere. For an orbit confined to this 3-sphere, the amplitude of the motion relative to the ecliptic (the plane of the orbits of Sun and Earth) can vary only slightly.
We show that we can obtain new orbits whose amplitude of motion relative to the ecliptic changes significantly, by following orbits of the flow restricted to the 3-sphere alternatively with homoclinic orbits that turn around the Earth. We provide an abstract theorem for the existence of such ‘diffusing’ orbits, and numerical evidence that the premises of the theorem are satisfied in the three-body problem considered here. We provide an explicit construction of diffusing orbits.
The geometric mechanism underlying this construction is reminiscent of the Arnold diffusion problem for Hamiltonian systems. Our argument, however, does not involve transition chains of tori as in the classical example of Arnold. We exploit mostly the ‘outer dynamics’ along homoclinic orbits, and use very little information on the ‘inner dynamics’ restricted to the 3-sphere.
As a possible application to astrodynamics, diffusing orbits as above can be used to design low cost maneuvers to change the inclination of an orbit of a satellite near L1 from a nearly-planar orbit to a tilted orbit with respect to the ecliptic. We explore different energy levels, and estimate the largest orbital inclination that can be achieved through our construction.