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DEIM-RR-08-005 (225.7Kb)
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Title

INVERSE APPROACH IN THE STUDY OF ORDINARY DIFFERENTIAL EQUATIONS

Author/s

Rafael O. Ramírez Inostroza and Natalia Sadovskaia

Date

07-10-2008

Research team

Sistemes Dinàmics

Research report type

Recerca

Language

Inglés

Number of pages

42

Summary

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. We propose the upper bound for the maximum degree of the invariant curve and for the maximum numbers of the algebraic limit cycles.

Keywords

Nonlinear ordinary differential equations, algebraic limit cycle.