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<creators>
<creator>
<creatorName>Popa, M.N.</creatorName>
<affiliation>Institutul de Matematică şi Informatică al AŞM, Moldova, Republica</affiliation>
</creator>
<creator>
<creatorName>Pricop, V.V.</creatorName>
<affiliation>Institutul de Matematică şi Informatică al AŞM, Moldova, Republica</affiliation>
</creator>
</creators>
<titles>
<title xml:lang='en'>Applications of algebraic methods in solving
the center-focus problem</title>
</titles>
<publisher>Instrumentul Bibliometric National</publisher>
<publicationYear>2013</publicationYear>
<relatedIdentifier relatedIdentifierType='ISSN' relationType='IsPartOf'>1024-7696</relatedIdentifier>
<subjects>
<subject>Differential systems</subject>
<subject>the center-focus problem</subject>
<subject>focal quantities</subject>
<subject>Sibirsky graded algebras</subject>
<subject>Hilbert serie</subject>
</subjects>
<dates>
<date dateType='Issued'>2013-09-03</date>
</dates>
<resourceType resourceTypeGeneral='Text'>Journal article</resourceType>
<descriptions>
<description xml:lang='en' descriptionType='Abstract'>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. ! · %.</description>
</descriptions>
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<format>application/pdf</format>
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</resource>