13 citations · 73 across the 22 of their papers we have counts for
26 papers
Algebraic Aspects of combined matrices
Primitivo B. Acosta-Humánez, Randy Leonardo, Máximo Santana
In this work, we present algebraic results concerning the combined matrices , where the entries of belong to a number field and is a non-singular matrix…
A note on the integrability of exceptional potentials via polynomial bi-homogeneous potentials
Primitivo B. Acosta-Humánez, Martha Álvarez-Ramírez, Teresinha J. Stuchi
This paper is concerned with the polynomial integrability of the two-dimensional Hamiltonian systems associated to complex homogeneous polynomial potentials of degree of type $…
Transcritical Bifurcations and Algebraic Aspects of Quadratic Multiparametric Families
Jorge Rodríguez Contreras, Alberto Reyes Linero, Bladimir Blanco Montes +1
This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in…
Non-integrability of the axisymmetric Bianchi IX cosmological model via Differential Galois Theory
Primitivo Acosta-Humánez, Juan J. Morales-Ruiz, Teresinha J. Stuchi
We investigate the integrability of an anisotropic universe with matter and cosmological constant formulated as Bianchi IX models. The presence of the cosmological constant causes…
From Poincaré to May: The Genesis of Discrete Dynamics
Oscar E. Martínez-Castiblanco, Primitivo B. Acosta-Humánez
In this paper, the origin of discrete dynamics is stated from a historical point of view, as well as its main ideas: fixed and periodic points, chaotic behaviour, bifurcations. Thi…
Liouvillian solutions for second order linear differential equations with Laurent polynomial coefficient
Primitivo B. Acosta-Humánez, David Blázquez-Sanz, Henock Venegas-Gómez
This paper is devoted to a complete parametric study of Liouvillian solutions of the general trace-free second order differential equation with a Laurent polynomial coefficient. Th…
Liouvillian solutions for second order linear differential equations with polynomial coefficients
Primitivo B. Acosta-Humánez, David Blázquez-Sanz, Henock Venegas-Gómez
In this paper we present an algebraic study concerning the general second order linear differential equation with polynomial coefficients. By means of Kovacic's algorithm and asymp…
Algebraic and qualitative aspects of quadratic vector fields related with classical orthogonal polynomials
Primitivo B Acosta-Humánez, Maria Campo Donado, Alberto Reyes Linero +1
This paper is a sequel of the reference \cite[§4.2, p.p. 1782--1783]{almp}, in where some families of quadratic polynomial vector fields related with orthogonal polynomials were st…
Nonintegrability of the unfoldings of codimension-two bifurcations
Primitivo B. Acosta-Humánez, Kazuyuki Yagasaki
Codimension-two bifurcations are fundamental and interesting phenomena in dynamical systems. Fold-Hopf and double-Hopf bifurcations are the most important among them. We study the…
Liouvillian Solutions of Schrödinger Equation with Polynomial Potentials using Gröbner Basis
Primitivo Belén Acosta-Humánez, Henock Venegas-Gómez
The main aim of this paper is the presentation of a new methodology to obtain Liouvillian solutions of stationary one dimensional Schrödinger equation with quasi-solvable polynomia…
Algebraic and qualitative remarks about the family
Primitivo B. Acosta-Humánez, Alberto Reyes-Linero, Jorge Rodríguez-Contreras
The aim of this paper is the analysis, from algebraic point of view and singularities studies, of the 5-parametric family of differential equations \begin{equation*}\label{folpz} y…
Generalized Lennard-Jones Potentials, SUSYQM and Differential Galois Theory
Manuel F. Acosta-Humánez, Primitivo B. Acosta-Humánez, Erick Tuirán
In this paper we start with proving that the Schrödinger equation (SE) with the classical Lennard-Jones (L-J) potential is nonintegrable in the sense of the differential Gal…
Variations for Some Painlevé Equations
Primitivo B. Acosta-Humánez, Marius van der Put, Jaap Top
This paper first discusses irreducibility of a Painlevé equation . We explain how the Painlevé property is helpful for the computation of special classical and algebraic solutio…
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness
Primitivo Acosta-Humánez, Hernán Giraldo, Carlos Piedrahita
The trajectory of energy is modeled by the solution of the Eikonal equation, which can be solved by solving a Hamiltonian system. This system is amenable of treatment from the poin…
Isomonodromy for the Degenerate Fifth Painlevé Equation
Primitivo B. Acosta-Humánez, Marius van der Put, Jaap Top
This is a sequel to papers by the last two authors making the Riemann-Hilbert correspondence and isomonodromy explicit. For the degenerate fifth Painlevé equation, the moduli space…
Pasting and Reversing Approach to Matrix Theory
Primitivo B. Acosta-Humánez, Adriana L. Chuquen
The aim of this paper is to study some aspects of matrix theory through Pasting and Reversing. We start giving a summary of previous results concerning to Pasting and Reversing ove…
Simple permutations with order by means of Pasting and Reversing
Primitivo B. Acosta-Humánez, Oscar E. Martínez-Castiblanco
The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Humánez \& Bernhardt (power of two). It is well known that Sharkovskii's theorem…
A model of anaerobic digestion for biogas production using Abel equations
Primitivo B. Acosta-Humánez, Maximiliano Machado-Higuera, Alexander V. Sinitsyn
Some time ago has been studied mathematical models for biogas production due to its importance in the use of control and optimization of re\-new\-able resources and clean energy. I…
Liouvillian Propagators, Riccati Equation and Differential Galois Theory
Primitivo B. Acosta-Humánez, Erwin Suazo
In this paper a Galoisian approach to build propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of…
Pasting and Reversing Operations over some Vector Spaces
Primitivo Acosta-Humánez, Adriana Lorena Chuquen, Ángela Mariette Rodríguez
Pasting and Reversing operations have been used successfully over the set of integer numbers, simple permutations, rings and recently over a generalized vector product. In this pap…
Some Remarks on a Generalized Vector Product
Primitivo B. Acosta-Humánez, Moisés Aranda, Reinaldo Núñez
In this paper we use a generalized vector product to construct an exterior form , where $\binom{n}{k}=\frac{n!}{(n-k)!k!…
Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations
Primitivo B. Acosta-Humánez, Chara Pantazi
In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the "invariance"…
Non-integrability Criterium for Normal Variational Equations around an integrable Subsystem and an example: The Wilbeforce spring-pendulum
Primitivo B. Acosta-Humánez, Martha Alvarez--Ramírez, David Blázquez-Sanz +1
In this paper we analyze the non-integrability of the Wilbeforce pendulum by means of Morales-Ramis theory in where is enough to prove that the Galois group of the variational equa…
On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory
Primitivo B. Acosta-Humánez, J. Tomás Lázaro-Ochoa, Juan J. Morales-Ruiz +1
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. I…