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<oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'>
<dc:creator>Popa, M.N.</dc:creator>
<dc:creator>Pricop, V.V.</dc:creator>
<dc:date>2013-09-03</dc:date>
<dc:description xml:lang='en'>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. ! · %.</dc:description>
<dc:source>Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica 71 (1) 45-71</dc:source>
<dc:subject>Differential systems</dc:subject>
<dc:subject>the center-focus problem</dc:subject>
<dc:subject>focal quantities</dc:subject>
<dc:subject>Sibirsky graded algebras</dc:subject>
<dc:subject>Hilbert serie</dc:subject>
<dc:title>Applications of algebraic methods in solving
the center-focus problem</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
</oai_dc:dc>