ON THE SERIES DEFINED BY DIFFERENTIAL EQUATIONS, WITH AN EXTENSION OF THE PUISEUX POLYGON CONSTRUCTION TO THESE EQUATIONS
From MaRDI portal
Publication:4290059
DOI10.1524/anly.1993.13.12.103zbMath0793.34009OpenAlexW2330180632MaRDI QIDQ4290059
Publication date: 28 April 1994
Published in: Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1524/anly.1993.13.12.103
Implicit ordinary differential equations, differential-algebraic equations (34A09) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Explicit solutions, first integrals of ordinary differential equations (34A05) Ordinary differential equations in the complex domain (34M99)
Related Items
Local simplification of first-order systems of ordinary differential equations of dimension two ⋮ Singularities of algebraic differential equations ⋮ Parabolic curves of diffeomorphisms asymptotic to formal invariant curves ⋮ On the convergence of generalized power series solutions of \(q\)-difference equations ⋮ On the convergence of generalized power series satisfying an algebraic ODE ⋮ Singular initial value problems for scalar quasi-linear ordinary differential equations ⋮ Multiplicity of the solutions of a differential polynomial ⋮ Detecting degenerate behaviors in first order algebraic differential equations ⋮ Power series solutions of non-linear \(q\)-difference equations and the Newton-Puiseux polygon ⋮ Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics ⋮ A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs ⋮ Blowings-Up of Vector Fields ⋮ Rational solutions of ordinary difference equations ⋮ An extension of the Newton-Puiseux polygon construction to give solutions of Pfaffian forms ⋮ A differential Puiseux theorem in generalized series fields of finite rank ⋮ Tropical differential Gröbner bases ⋮ An analytic proof of the Malgrange theorem on the convergence of formal solutions of an ODE ⋮ Reduction of singularities of three-dimensional line foliations ⋮ About the cover: The Fine–Petrović Polygons and the Newton–Puiseux Method for Algebraic Ordinary Differential Equations ⋮ Convergence of formal Dulac series satisfying an algebraic ordinary differential equation ⋮ Generalised power series solutions of sub-analytic differential equations
