9 citations · 18 across the 12 of their papers we have counts for
14 papers
Dynamics of Kahan-Hirota-Kimura maps with rational invariant fibrations
Víctor Mañosa, Chara Pantazi
We present a simple method to study the dynamics of planar Kahan-Hirota-Kimura (KHK) maps preserving rational fibrations. Using this approach, we show that integrable KHK maps may…
Liouvillian integrability of vector fields in higher dimensions
Waleed Aziz, Colin Christopher, Chara Pantazi +1
We consider complex rational vector fields in dimension (equivalently, differential forms of degree in variables) which admit a Liouvillian first integral. Extendin…
Liouvillian integrability of rational vector fields: The case of algebraic extensions
Colin Christopher, Chara Pantazi, Sebastian Walcher
As shown in a previous paper, whenever a rational vector field on , , is Liouvillian integrable, then it admits a first integral obtained by two successive integr…
Kahan-Hirota-Kimura maps preserving original cubic hamiltonians
Víctor Mañosa, Chara Pantazi
We study the class of cubic Hamiltonian vector fields whose associated Kahan-Hirota-Kimura (KHK) maps preserve the original Hamiltonian function. Our analysis focuses on these fiel…
Liouvillian integrability of three dimensional vector fields
Waleed Aziz, Colin Christopher, Chara Pantazi +1
We consider a three dimensional complex polynomial, or rational, vector field (equivalently, a two-form in three variables) which admits a Liouvillian first integral. We prove that…
Semiclassical quantification of some two degree of freedom potentials: a Differential Galois approach
P. B. Acosta-Humánez, J. T. Lázaro, J. J. Morales-Ruiz +1
In this work we explain the relevance of the Differential Galois Theory in the semiclassical (or WKB) quantification of some two degree of freedom potentials. The key point is that…
Darboux integrability and dynamics of the Basener-Ross population model
Faruk Güngör, Jaume Llibre, Chara Pantazi
We deal with the Basener and Ross model for the evolution of human population in Easter island. We study the Darboux integrability of this model and characterize all its global dyn…
Invariant algebraic surfaces of polynomial vector fields in dimension three
Niclas Kruff, Jaume Llibre, Chara Pantazi +1
We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a clas…
Differential Galois Theory and non-Integrability of Planar Polynomial Vector Fields
Primitivo B. Acosta-Humánez, J. Tomás Lázaro, Juan J. Morales-Ruiz +1
We study a necessary condition for the integrability of the polynomials fields in the plane by means of the differential Galois theory. More concretely, by means of the variational…
Limit cycles bifurcating from a degenerate center
J. Llibre, C. Pantazi
We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second…
Analytic integrability of the Bianchi Class A cosmological models with 0<= k<1
Antoni Ferragut, Jaume Llibre, Chara Pantazi
There are many works studying the integrability of the Bianchi class A cosmologies with k=1. Here we characterize the analytic integrability of the Bianchi class A cosmological mod…
The Picard Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
Yuri Fedorov, Chara Pantazi
We consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the system of 5 linear ODEs for periods of the corresponding Abelian integrals of first, se…
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"…
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…