﻿ ﻿﻿ The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials
 Conţinutul numărului revistei Articolul precedent Articolul urmator 461 1 Ultima descărcare din IBN: 2020-01-09 10:08 Căutarea după subiecte similare conform CZU 515+517.9 (1) Mathematics (1245) Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (171) SM ISO690:2012SCHLOMIUK, Dana; VULPE, Nicolae. The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2019, nr. 2(90), pp. 41-55. ISSN 1024-7696. EXPORT metadate: Google Scholar Crossref CERIF DataCiteDublin Core
Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 2(90) / 2019 / ISSN 1024-7696

 The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials
CZU: 515+517.9
MSC 2010: 58K45, 34C05, 34C23, 34A34.

Pag. 41-55

 Schlomiuk Dana1, Vulpe Nicolae2 1 Université de Montréal,2 Vladimir Andrunachievici Institute of Mathematics and Computer Science Disponibil în IBN: 3 ianuarie 2020

Rezumat

In this paper we provide affine invariant necessary and sufficient conditions for a non-degenerate quadratic differential system to have an invariant conic f(x, y) = 0 and a Darboux invariant of the form f(x, y)est with , s ∈ R and s 6= 0. The family of all such systems has a total of seven topologically distinct phase portraits. For each one of these seven phase portraits we provide necessary and sufficient conditions in terms of affine invariant polynomials for a non-degenerate quadratic system in this family to possess this phase portrait.

Cuvinte-cheie
quadratic differential system, invariant conic, Darboux invariant, affine invariant polynomial, Group action, phase portrait

### Cerif XML Export

<?xml version='1.0' encoding='utf-8'?>
<CERIF xmlns='urn:xmlns:org:eurocris:cerif-1.5-1' xsi:schemaLocation='urn:xmlns:org:eurocris:cerif-1.5-1 http://www.eurocris.org/Uploads/Web%20pages/CERIF-1.5/CERIF_1.5_1.xsd' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' release='1.5' date='2012-10-07' sourceDatabase='Output Profile'>
<cfResPubl>
<cfResPublId>ibn-ResPubl-91138</cfResPublId>
<cfResPublDate>2019-12-27</cfResPublDate>
<cfVol>90</cfVol>
<cfIssue>2</cfIssue>
<cfStartPage>41</cfStartPage>
<cfISSN>1024-7696</cfISSN>
<cfURI>https://ibn.idsi.md/ro/vizualizare_articol/91138</cfURI>
<cfTitle cfLangCode='EN' cfTrans='o'><p>The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials</p></cfTitle>
<cfKeyw cfLangCode='EN' cfTrans='o'>quadratic differential system; invariant conic; Darboux
invariant; affine invariant polynomial; Group action; phase portrait</cfKeyw>
<cfAbstr cfLangCode='EN' cfTrans='o'><p>In this paper we provide affine invariant necessary and sufficient conditions for a non-degenerate quadratic differential system to have an invariant conic f(x, y) = 0 and a Darboux invariant of the form f(x, y)est with , s &isin; R and s 6= 0. The family of all such systems has a total of seven topologically distinct phase portraits. For each one of these seven phase portraits we provide necessary and sufficient conditions in terms of affine invariant polynomials for a non-degenerate quadratic system in this family to possess this phase portrait.</p></cfAbstr>
<cfResPubl_Class>
<cfClassId>eda2d9e9-34c5-11e1-b86c-0800200c9a66</cfClassId>
<cfClassSchemeId>759af938-34ae-11e1-b86c-0800200c9a66</cfClassSchemeId>
<cfStartDate>2019-12-27T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfResPubl_Class>
<cfClassId>e601872f-4b7e-4d88-929f-7df027b226c9</cfClassId>
<cfClassSchemeId>40e90e2f-446d-460a-98e5-5dce57550c48</cfClassSchemeId>
<cfStartDate>2019-12-27T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfPers_ResPubl>
<cfPersId>ibn-person-14974</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfStartDate>2019-12-27T24:00:00</cfStartDate>
</cfPers_ResPubl>
<cfPers_ResPubl>
<cfPersId>ibn-person-657</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfStartDate>2019-12-27T24:00:00</cfStartDate>
</cfPers_ResPubl>
</cfResPubl>
<cfPers>
<cfPersId>ibn-Pers-14974</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-14974-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2019-12-27T24:00:00</cfStartDate>
<cfFamilyNames>Schlomiuk</cfFamilyNames>
<cfFirstNames>Dana</cfFirstNames>
</cfPersName_Pers>
</cfPers>
<cfPers>
<cfPersId>ibn-Pers-657</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-657-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2019-12-27T24:00:00</cfStartDate>
<cfFamilyNames>Vulpe</cfFamilyNames>
<cfFirstNames>Nicolae</cfFirstNames>
</cfPersName_Pers>
</cfPers>
</CERIF>