Cubic differential systems with two affine real non-parallel invariant straight lines of maximal multiplicity
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517.9+517.925.41 (1)
Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (245)
SM ISO690:2012
VACARAŞ, Olga. Cubic differential systems with two affine real non-parallel invariant straight lines of maximal multiplicity. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2015, nr. 3(79), pp. 79-101. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 3(79) / 2015 / ISSN 1024-7696 /ISSNe 2587-4322

Cubic differential systems with two affine real non-parallel invariant straight lines of maximal multiplicity
CZU: 517.9+517.925.41

Pag. 79-101

Vacaraş Olga
 
Institute of Mathematics and Computer Science ASM
 
Proiecte:
 
Disponibil în IBN: 10 iunie 2016


Rezumat

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), m1(2, 1; 3), m1(1, 1; 3) are determined. The normal forms and the corresponding perturbations of the cubic systems which realize these cases are given.

Cuvinte-cheie
Cubic differential system, invariant straight line,

algebraic multiplicity,

geometric multiplicity.