Research report: DEIM-RR-08-005
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.
