REZOLVAREA PROBLEMEI CENTRULUI PENTRU UN SISTEM DIFERENŢIAL CUBIC CE ARE O DREAPTĂ INVARIANTĂ REALĂ ŞI LINIA DE LA INFINIT DE MULTIPLICITATEA DOI

Alexandru ŞUBĂ; Alexandru PÎSLARU

doi:10.36120/2587-3644.v8i2.76-83

Vol 8 No 2 (2019), Статьи

Vol 8 No 2 (2019)

SOLUTION OF THE CENTER-FOCUS PROBLEM FOR A CUBIC DIFFERENTIAL SYSTEM WITH A REAL INVARIANT STRAIGHT LINE AND THE LINE AT INFINITY OF MULTIPLICITY TWO

Статьи

https://doi.org/10.36120/2587-3644.v8i2.76-83

Published January 28, 2020

Alexandru ŞUBĂ⁺⁻
Alexandru PÎSLARU⁺⁻

Alexandru ŞUBĂ

Tiraspol State University

Alexandru PÎSLARU

Tiraspol State University

Supplementary Files

pdf (Русский)

Keywords

cubic differential system, invariant straight line, multiplicity, the center problem.

How to Cite

ŞUBĂ, A., & PÎSLARU, A. (2020). SOLUTION OF THE CENTER-FOCUS PROBLEM FOR A CUBIC DIFFERENTIAL SYSTEM WITH A REAL INVARIANT STRAIGHT LINE AND THE LINE AT INFINITY OF MULTIPLICITY TWO. Acta Et Commentationes Exact and Natural Sciences, 8(2), 76-83. https://doi.org/10.36120/2587-3644.v8i2.76-83

Abstract

In this paper, we show that for cubic differential system x = y(x − 1) 2 , y = −(x + gx2 +dxy + by 2 + qx 2y) the critical point (0,0) is a center if and only if the first four Lyapunov quantities vanish (L1 = L2 = L3 = L4 = 0) or, equivalently, if at least one of the following two sets of conditions: 1) b = 0, q = dg; 2) d = q = 0 holds.

Mathematics Subject Classification (2010): 34C05.