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Center conditions to find certain degenerate centers with characteristic directions
Algaba Durán, Antonio
; García García, Cristóbal; Giné, Jaume (Elsevier, 2023)
We consider the two-dimensional autonomous systems of differential equations where the origin is a monodromic degenerate singular point, i.e., with null linear part. In this work we give two heuristic procedures to obtain ... -
A Value for Graph-Restricted Games with Middlemen on Edges
(MDPI, 2022)In a cooperative game with a communication structure, a graph describes the communication possibilities of the players, which are represented by the nodes. We introduce a variation of this model by assuming that each ... -
Study of a homoclinic canard explosion from a degenerate center
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba Durán, Antonio; Rodríguez Luis, Alejandro José (Elsevier, 2022)
Canard explosion is an appealing event occurring in singularly perturbed systems. In this phenomenon, upon variation of a parameter within an exponentially small range, the amplitude of a small limit cycle increases ... -
Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system
Algaba Durán, Antonio; Domínguez Moreno, María Cinta; Merino Morlesín, Manuel; Rodríguez Luis, Alejandro José (Elsevier, 2022)
In this paper we consider a 3D three-parameter unfolding close to the normal form of the triple-zero bifurcation exhibited by the Lorenz system. First we study analytically the double-zero degeneracy (a double-zero ... -
Matemáticas en contexto en Educación Primaria: conexiones con el entorno y la música
Alsina, Ángel; Contreras, Manuela; Reyes Columé, Joaquín (Federación Iberoamericana de Sociedades de Educación Matemática (FISEM), 2022-04)
Se describe un enfoque competencial de la enseñanza de las matemáticas en Educación Primaria a partir de actividades contextualizadas. Para ello, en la primera parte se fundamenta teóricamente el conocimiento pedagógico ... -
Analytic partial-integrability of a symmetric Hopf-zero degeneracy
Algaba Durán, Antonio; García García, Cristóbal; Reyes Columé, Manuel (Cambridge University Press, 2022)
We deal with analytic three-dimensional symmetric systems whose origin is a Hopf-zero singularity. Once it is not completely analytically integrable, we provide criteria on the existence of at least one functionally ... -
On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere
(World Scientific Publishing, 2022)Based on the presentation of the Kauffman bracket skein algebra of the thickened torus given by the third author in previous work [4], Frohman and Gelca established a complete description of the multiplicative operation ... -
Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor
Algaba Durán, Antonio; García García, Cristóbal; Giné, Jaume (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
Algaba Durán, Antonio; García García, Cristóbal; Giné, Jaume (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
Algaba Durán, Antonio; García García, Cristóbal; Giné, Jaume (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
Algaba Durán, Antonio; Checa Camacho, Isabel; García García, Cristóbal; Giné, Jaume (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
Algaba Durán, Antonio; Fuentes Díaz, Natalia; Gamero, Estanislao; García García, Cristóbal (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
Algaba Durán, Antonio; Díaz García, María; García García, Cristóbal; Giné, Jaume (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
Algaba Durán, Antonio; García García, Cristóbal, Matemático; Reyes Columé, Manuel (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
Algaba Durán, Antonio; García García, Cristóbal; Giné, Jaume (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
Algaba Durán, Antonio; Gamero, Estanislao; García García, Cristóbal (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
Algaba Durán, Antonio; García García, Cristóbal; Giné, Jaume (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?
Romero Sánchez, Sixto (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
Romero Sánchez, Sixto; Rodríguez García, Isabel María; Benítez Cambra, Rocío; Salas Martín, Isabel Mª (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 ...
