Departamento de Matemáticas
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Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor
(Elsevier, 2019)In this work is characterized the analytic integrability problem around a nilpotent singularity for differential systems in the plane under generic conditions. The analytic integrability problem is characterized via the ... -
On the Formal Integrability Problem for Planar Differential Systems
(Hindawi Publishing Corporation, 2013)We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, ... -
Analytic Integrability of Some Examples of Degenerate Planar Vector Fields
(Springer, 2016)This paper is devoted to the classification of analytic integrable cases of two families of degenerate planar vector fields with a monodromic singular point at the origin. This study falls in the still open degenerate ... -
Analytic integrability inside a family of degenerate centers
(Elsevier, 2016)In this paper we study the analytic integrability around the origin inside a family of degenerate centers or perturbations of them. For this family analytic integrability does not imply formal orbital equivalence to a ... -
On the Integrability Problem for the Hopf-Zero singularity and its relation with the inverse Jacobi multiplier
(Elsevier, 2021)In this paper we use the orbital normal form of the nondegenerate Hopf-zero singularity to obtain necessary conditions for the existence of first integrals for such singularity. Also, we analyze the relation between the ... -
Center problem for generic degenerate vector fields
(Elsevier, 2022)We generalize the method of construction of an integrating factor for Abel differential equations, developed in Briskin et al. (1998), for any generic monodromic singularity. Here generic means that the vector field has ... -
Algebraic integrability of nilpotent planar vector fields
(Elsevier, 2021)We characterize, using normal forms of quasi-homogeneous expansions, the analytic vector fields at nilpotent singular point having an algebraic first integral over the ring C [[ x, y ]] . As a consequence, we provide a ... -
A New Normal Form for Monodromic Nilpotent Singularities of Planar Vector Fields
(Springer, 2021)In this work, we present a new technique for solving the center problem for nilpotent singularities which consists of determining a new normal form conveniently adapted to study the center problem for this singularity. In ... -
Orbital Hypernormal Forms
(MDPI, 2021)In this paper, we analyze the problem of determining orbital hypernormal forms—that is, the simplest analytical expression that can be obtained for a given autonomous system around an isolated equilibrium point through ... -
Orbital Reversibility of Planar Vector Fields
(MDPI, 2021-01)In this work we use the normal form theory to establish an algorithm to determine if a planar vector field is orbitally reversible. In previous works only algorithms to determine the reversibility and conjugate reversibility ... -
The Root Extraction Problem for Generic Braids
(MDPI, 2019-11)We show that, generically, finding the k-th root of a braid is very fast. More precisely, we provide an algorithm which, given a braid x on n strands and canonical length l, and an integer k > 1, computes a k-th root of ... -
RINCÓN “SAPERE AUDE”… ¿resolviendo problemas?
(Sociedad Andaluza de Educación Matemática THALES, 2019-08)En este número incluimos, aparte de la sección de Joyitas (denominación a los ejercicios que se plantean y resuelven en la segunda parte del artículo) una primera con un breve bosquejo sobre historia de las Matemáticas en ... -
La resolución de problemas como instrumentos para la modelización matemática : Ejemplos para la vida real
(Universitat Politècnica de València, 2015-12)No hace muchos años que los investigadores en Educación Matemática han centrado su atención en el diseño de actividades basado en la modelización matemática de situaciones reales con el convencimiento de obtener una mayor ... -
Modelización matemática en secundaria desde un punto de vista superior: EL PROBLEMA DE DOBOGÓKÓ
(Universitat Politècnica de València, 2008-12)El presente trabajo describe y analiza una experiencia de modelización matemática que bien podría desarrollarse en el aula con alumnos de secundaria. Las distintas etapas del proceso de modelización seguido se describen ... -
La resolución de problemas como herramienta para la modelización matemática
(Universitat Politècnica de València, 2011-12)La conexión entre las matemáticas y la realidad que nos rodea se ejecuta por medio de actividades de la resolución de problemas contextualizados en nuestro entorno de vida. No hay que olvidar que la Matemática ha evolucionado ... -
Control borroso multivariable basado en heurística. Un caso práctico: grúa porta contenedores
(Comité Español de Autonomática (CEA-IFAC), 2007-07)En este trabajo se presenta el diseño de un controlador borroso basado en heurística: conocimiento de la planta e incorporación del conocimiento de un experto (gruísta), que permite automatizar el proceso de carga de ... -
p-continuous vector–valued functions
(Universidad de Huelva, 2017)This thesis focuses on the study of p-continuous vector-valued functions. They are functions defined on a compact Hausdorff space with values in a Banach space whose range is p-compact (1 < p < oo). A subset K of a Banach ... -
Contribution to the qualitative theory of dynamical systems
(Universidad de Huelva, 2017)En esta memoria abordamos tres problemas fundamentales dentro de ia teoría cualitativa de sistemas dinámicos. En un sentido amplio, el objetivo de la teoría de sistemas dinámicos es determinar la estructura del conjunto ... -
Integrability of two dimensional quasi-homogeneous polynomial differential systems
(Rocky Mountain Mathematics Consortium, 2011)In terms of the conservative-dissipative de composition of a vector field, we characterize the two dimensional quasi-homogeneous polynomial differential systems with a polynomial first integral (in these systems, polynomial ... -
Nilpotent Systems Admitting an Algebraic Inverse Integrating Factor over C((x,y))
(Springer Verlag, 2011)We characterize the nilpotent systems whose lowest degree quasihomogeneous term is (y, σ xn)T, σ = ±1, which have an algebraic inverse integrating factor over C((x,y)) . In such cases, we show that the systems admit an ...