Thesis Collection
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Browsing by Author "García García, Cristóbal, Matemático"
Now showing items 1-14 of 14
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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 ... -
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 ... -
Analysis of dynamical systems via normal forms
Fuentes Díaz, Natalia (Universidad de Huelva, 2015)
Desde hace muchos años los problemas de la dinámica han sido objeto de estudio por científicos de distintas épocas. Podemos decir que los sistemas dinámicos se ocupan del estudio de los modelos de evolución de los sistemas ... -
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 ... -
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 ... -
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 ... -
Contribution to the qualitative theory of dynamical systems
Checa Camacho, Isabel (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 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 ... -
Integrability of two dimensional quasi-homogeneous polynomial differential systems
Algaba Durán, Antonio; García García, Cristóbal, Matemático; Reyes Columé, Manuel (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))
Algaba Durán, Antonio; García García, Cristóbal, Matemático; Reyes Columé, Manuel (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 ... -
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, ... -
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 ... -
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 ...
