We present a review of results of the so-called Painlevé singularity approach to the
investigation of the integrability of dynamical systems with finite and infinite number of …

In recent investigations on nonlinear dynamics, the singularity structure analysis pioneered
by Kovalevskaya, Painlevé and contempories, which stresses the meromorphic nature of the …

This invaluable book examines qualitative and quantitative methods for nonlinear differential
equations, as well as integrability and nonintegrability theory. Starting from the idea of a …

The characteristic feature of the so‐called Painlevé test for integrability of an ordinary (or
partial) analytic differential equation, as usually carried out, is to determine whether all its …

This book aims to present a new approach called Flow Curvature Method that applies
Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any …

Nonlinear ordinary differential equations appear in many branches of applied mathematics,
physics and, in general, in applied sciences. For a differential system or a vector field …

Darboux integrability and invariant algebraic curves for planar polynomial systems Page 1
INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND …

We describe the improved Darboux theory of integrability for polynomial ordinary differential
equations in three dimensions. Using this theory and computer algebra, we study the …

A method already introduced by the last two authors for finding the integrable cases of three-
dimensional autonomous ordinary differential equations based on the Frobenius …

We consider the class of polynomial differential equations x˙= λx+ Pn (x, y), y˙= λy+ Qn (x, y),
in R2 where Pn (x, y) and Qn (x, y) are homogeneous polynomials of degree n> 1 and λ≠ 0 …