We show how the use of rational parameterizations facilitates the study of the number of solutions of many systems of equations involving polynomials and square roots of polynomials. We illustrate the effectiveness of this approach, applying it to several problems appearing in the study of some dynamical systems. Our examples include Abelian integrals, Melnikov functions and a couple of questions in Celestial Mechanics: the computation of some relative equilibria and the study of some central configurations
AbstractGiven a system of polynomial equations and inequations with coefficients in the field of rat...
AbstractA method to generate accurate approximations to the singular solutions of a system of (compl...
Given a system of polynomial equations and inequations with coefficients in the field of rational nu...
We show how the use of rational parameterizations facilitates the study of the number of solutions o...
In this work, Laurent series expansion compared with definition of rational function is used to find...
19 pages, 4 algorithms, 4 tables, 1 figureDetailed dynamical systems models used in life sciences ma...
The celebrated Hilbert\u27s 10th problem asks for an algorithm to decide whether a system of po...
. In this paper we analyse the dynamics of a family of rational operators coming from a fourth-orde...
Systems of polynomial equations arise naturally from many problems in applied mathematics and engine...
In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order f...
University of Minnesota Ph.D. dissertation. April 2011. Major: Mathematics. Advisor: Richard Moeckel...
AbstractIn this paper, we provide an algorithm to compute explicit rational solutions of a rational ...
“The use of rational polynomials for approximating surfaces is investigated in this study. In partic...
AbstractA new technique for the geometry of numbers is exhibited. This technique provides sharp esti...
Abstract. We give a necessary and sufficient condition for an ODE to have a rational type general so...
AbstractGiven a system of polynomial equations and inequations with coefficients in the field of rat...
AbstractA method to generate accurate approximations to the singular solutions of a system of (compl...
Given a system of polynomial equations and inequations with coefficients in the field of rational nu...
We show how the use of rational parameterizations facilitates the study of the number of solutions o...
In this work, Laurent series expansion compared with definition of rational function is used to find...
19 pages, 4 algorithms, 4 tables, 1 figureDetailed dynamical systems models used in life sciences ma...
The celebrated Hilbert\u27s 10th problem asks for an algorithm to decide whether a system of po...
. In this paper we analyse the dynamics of a family of rational operators coming from a fourth-orde...
Systems of polynomial equations arise naturally from many problems in applied mathematics and engine...
In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order f...
University of Minnesota Ph.D. dissertation. April 2011. Major: Mathematics. Advisor: Richard Moeckel...
AbstractIn this paper, we provide an algorithm to compute explicit rational solutions of a rational ...
“The use of rational polynomials for approximating surfaces is investigated in this study. In partic...
AbstractA new technique for the geometry of numbers is exhibited. This technique provides sharp esti...
Abstract. We give a necessary and sufficient condition for an ODE to have a rational type general so...
AbstractGiven a system of polynomial equations and inequations with coefficients in the field of rat...
AbstractA method to generate accurate approximations to the singular solutions of a system of (compl...
Given a system of polynomial equations and inequations with coefficients in the field of rational nu...