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Report de recerca: DEIM-RR-08-005

Descarrega
DEIM-RR-08-005 (225.7Kb)
Nombre de descàrregues: 1780

Títol

INVERSE APPROACH IN THE STUDY OF ORDINARY DIFFERENTIAL EQUATIONS

Autor/s

Rafael O. Ramrez Inostroza and Natalia Sadovskaia

Data

07-10-2008

Grup de recerca

Sistemes Dinmics

Tipus de report

Recerca

Idioma

Ingls

Nombre de pàgines

42

Resum

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.

Paraules Clau

Nonlinear ordinary differential equations, algebraic limit cycle.