Applications of algebraic methods in solving the center-focus problem
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2018-07-18 20:47
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POPA, Mihail; PRICOP, Victor. Applications of algebraic methods in solving the center-focus problem. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2013, nr. 1(71), pp. 45-71. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 1(71) / 2013 / ISSN 1024-7696

Applications of algebraic methods in solving the center-focus problem

Pag. 45-71

Popa Mihail, Pricop Victor
 
Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 15 decembrie 2013


Rezumat

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 center-focus 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 center-focus problem for this differential system does not exceed %, i. e. ! · %.

Cuvinte-cheie
Differential systems, focal quantities, Sibirsky graded algebras,

the center-focus problem, Hilbert serie