The problem of the centre for cubic systems with two parallel invariant straight lines and one invariant conic

Cozma Dumitru

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SM ISO690:2012

COZMA, Dumitru. The problem of the centre for cubic systems with two parallel invariant straight lines and one invariant conic. In: Nonlinear Differential Equations and Applications NoDEA, 2009, vol. 16, pp. 213-234. ISSN 1021-9722. DOI: https://doi.org/10.1007/s00030-008-7044-x

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Nonlinear Differential Equations and Applications NoDEA

Volumul 16 / 2009 / ISSN 1021-9722 /ISSNe 1420-9004

The problem of the centre for cubic systems with two parallel invariant straight lines and one invariant conic

DOI:https://doi.org/10.1007/s00030-008-7044-x

Pag. 213-234

Cozma Dumitru

Tiraspol State University

Proiecte:

12.839.08.05F Probleme de studiu local şi global al singularităţilor cîmpurilor vectoriale polinomiale

Disponibil în IBN: 13 septembrie 2023

Rezumat

For cubic differential systems with two parallel invariant straight lines and at least one invariant conic it is proved that a singular point with pure imaginary eigenvalues (a weak focus) is a centre if and only if the first three Liapunov quantities L _j , j = 1, 2, 3 vanish.

Cuvinte-cheie
Center-focus problem, Cubic differential systems, integrability., invariant algebraic curves

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