Integrability conditions for a class of cubic differential systems with a bundle of two invariant straight lines and one invariant cubic
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517.925 (42)
Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (242)
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COZMA, Dumitru, DASCALESCU, Anatolii. Integrability conditions for a class of cubic differential systems with a bundle of two invariant straight lines and one invariant cubic. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, vol. 86, nr. 1(86), pp. 120-138. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Volumul 86, Numărul 1(86) / 2018 / ISSN 1024-7696 /ISSNe 2587-4322

Integrability conditions for a class of cubic differential systems with a bundle of two invariant straight lines and one invariant cubic

CZU: 517.925
MSC 2010: 34C05.

Pag. 120-138

Cozma Dumitru1, Dascalescu Anatolii2
 
1 Tiraspol State University,
2 Institute of Mathematics and Computer Science ASM
 
Proiecte:
 
Disponibil în IBN: 26 iulie 2018


Rezumat

We determine conditions for the origin to be a center for a class of cubic differential systems having a bundle of two invariant straight lines and one invariant cubic. We prove that a fine focus O(0, 0) is a center if and only if the first three Lyapunov quantities vanish.

Cuvinte-cheie
Cubic differential system, Center-focus problem, invariant algebraic curve, integrability.