Conţinutul numărului revistei |
Articolul precedent |
Articolul urmator |
900 9 |
Ultima descărcare din IBN: 2021-11-14 00:58 |
Căutarea după subiecte similare conform CZU |
517.9 (244) |
Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (242) |
SM ISO690:2012 CIOBAN, Mitrofan, ROTARU, Tatiana. 130 de ani de zbucium pentru soluţionarea
problemei lui Poincaré despre centru şi focar
. In: Revista de Ştiinţă, Inovare, Cultură şi Artă „Akademos”, 2013, nr. 3(30), pp. 13-21. ISSN 1857-0461. |
EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
Revista de Ştiinţă, Inovare, Cultură şi Artă „Akademos” | ||||||
Numărul 3(30) / 2013 / ISSN 1857-0461 /ISSNe 2587-3687 | ||||||
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CZU: 517.9 | ||||||
Pag. 13-21 | ||||||
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Rezumat | ||||||
It is well known that many mathematical models use differential equation systems and apply the qualitative theory of differential equations, introduced by Poincaré and Liapunov. One of the problems that persists in order to control the behavior of systems of this type, is to distinguish between a focus or a center (the center-focus problem). The solving of this problem goes through the
computation of the Poincaré-Liapunov constants. In the case of polynomial right-hand sides it follows from Hilbert’s theorem on the fi niteness of bases of polynomial ideals that in this sequence only fi nitely many are essential and that the remaining ones are consequences of them. Hence, this problem is divided in two parts: in the fi rst, to estimate the number
of essential constants; in the second, to determine the
minimal upper border of the indexes of a complete system of essential constants. The fi rst part is called the weak center-focus problem. The problem of exitimation the maximal number of algebraically independent essential constants
is called the generalized center-focus problem. Recently
M. N.Popa and V. V. Pricop have solved the generalized center-focus problem. The present article contains: some moments related to the history of the center-focus problem; the contribution of the Sibirschi’s school in the solving of the center-focus problem; methodological aspects of the Popa – Pricop solution of the generalized center-focus problem. The problem of the estimation of the minimal upper border of the indexes of a complete system of algebraically independent essential constants is open. Another open problem consists on determining what differential systems are integrable. |
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Cuvinte-cheie Poincaré-Liapunov constants, centerfocus problem, generalized center-focus problem. |
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