Inverse Approach In The Study Of Ordinary Differential Equations

Details Inverse Approach In The Study Of Ordinary Differential Equations Inverse Approach In The Study Of Ordinary Differential Equations

2009-02-26

arxiv.org/abs/0902.4649v1

Mathematics

Dynamical Systems

Scientific paper

We extend the Eruguin result exposed in the paper "Construction of the whole set of ordinary differential equations with a given integral curve" published in 1952 and construct a differential system in $\Bbb{R}^N$ which admits a given set of the partial integrals, in particular we study the case when theses functions are polynomials. We construct a non-Darboux integrable planar polynomial system of degree $n$ with one invariant irreducible algebraic curve $g(x,y)=0$. For this system we analyze the Darboux integrability, Poincare's problem and 16th's Hilbert problem for algebraic limit cycles.

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