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SM ISO690:2012 POPA, Mihail; PRICOP, Victor. Applications of algebraic methods in solving
the centerfocus problem. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2013, nr. 1(71), pp. 4571. ISSN 10247696. 
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica  
Numărul 1(71) / 2013 / ISSN 10247696  


Pag. 4571  


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The nonlinear differential system x_ =P`i=0 Pmi (x; y); y_ =
P`i=0 Qmi (x; y) is considered, where Pmi and Qmi are homogeneous polynomials of degree mi ¸ 1 in x and y, m0 = 1. The set f1;mig`i=1 consists of a finite number (l < 1) of distinct
integer numbers. It is shown that the maximal number of algebraically independent focal quantities that take part in solving the centerfocus problem for the given differential
system with m0 = 1, having at the origin of coordinates a singular point of the second type (center or focus), does not exceed % = 2(
P`i=1mi `) 3: We make an assumption that the number ! of essential conditions for center which solve the centerfocus problem for this differential system does not exceed %, i. e. ! · %. 

Cuvintecheie Differential systems, focal quantities, Sibirsky graded algebras, the centerfocus problem, Hilbert serie 

