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IMI/Publicaţii/BASM/Ediţii/BASM n.3 (79), 2015/

Cubic differential systems with two affine real non-parallel invariant straight lines of maximal multiplicity

Authors: Vacaraş Olga

Abstract

In this article we classify all differential real cubic systems possessing two affine real non-parallel invariant straight lines of maximal multiplicity. We show that the maximal multiplicity of each of these lines is at most three. The maximal sequences of multiplicities: $m(3,3;1)$, $m(3,2;2)$, $m(3,1;3)$, $m(2,2;3)$, $m_{\infty}(2,1;3)$, $m_{\infty}(1,1;3)$ are determined. The normal forms and the corresponding perturbations of the cubic systems which realize these cases are given.

Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5 Academiei str., Chisinau, MD 2028
Moldova
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