Integrability conditions for a cubic differential system with two invariant straight lines and one invariant cubic
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DASCALESCU, Anatolii. Integrability conditions for a cubic differential system with two invariant straight lines and one invariant cubic. In: Annals of the University of Craiova, Mathematics and Computer Science Series, 2018, nr. 2(45), pp. 312-322. ISSN 1223-6934.
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Annals of the University of Craiova, Mathematics and Computer Science Series
Numărul 2(45) / 2018 / ISSN 1223-6934

Integrability conditions for a cubic differential system with two invariant straight lines and one invariant cubic


Pag. 312-322

Dascalescu Anatolii
 
Tiraspol State University
 
 
Disponibil în IBN: 24 iunie 2019


Rezumat

We find conditions for a singular point O(0; 0) of a center or a focus type to be a center, in a cubic differential system with two invariant straight lines and one invariant cubic. The presence of a center at O(0; 0) is proved by constructing Darboux first integrals.

Cuvinte-cheie
Cubic differential system, Darboux integrability, invariant algebraic curves, The problem of the center