7 citations · 7 across the 5 of their papers we have counts for
5 papers
Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
Jose Cano, Sebastian Falkensteiner, Daniel Robertz +1
In this paper we study systems of autonomous algebraic ODEs in several differential indeterminates. We develop a notion of algebraic dimension of such systems by considering them a…
Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs -- A MAPLE Package
Francois Boulier, Jose Cano, Sebastian Falkensteiner +1
There exist several methods for computing exact solutions of algebraic differential equations. Most of the methods, however, do not ensure existence and uniqueness of the solutions…
The local Poincaré problem for irreducible branches
José Cano, Pedro Fortuny Ayuso, Javier Ribón
Let be a germ of holomorphic foliation defined in a neighborhood of the origin of that has a germ of irreducible holomorphic invariant curve . W…
Existence and convergence of Puiseux series solutions for autonomous first order differential equations
Jose Cano, Sebastian Falkensteiner, J. Rafael Sendra
Given an autonomous first order algebraic ordinary differential equation F(y,y')=0, we prove that every formal Puiseux series solution, expanded around any finite point or at infin…
Power Series Solutions of Non-Linear q-Difference Equations and the Newton-Puiseux Polygon
José Cano, Pedro Fortuny Ayuso
Adapting the Newton-Puiseux Polygon process to nonlinear q-difference equations of any order and degree, we compute their power series solutions, study the properties of the set of…