書(shū)目名稱 | Global Bifurcation Theory and Hilbert’s Sixteenth Problem | 編輯 | Valery A. Gaiko | 視頻video | http://file.papertrans.cn/387/386043/386043.mp4 | 叢書(shū)名稱 | Mathematics and Its Applications | 圖書(shū)封面 |  | 描述 | On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second Interna- tional Congress of Mathematicians in Paris. The talk covered practically all directions of mathematical thought of that time and contained a list of 23 problems which determined the further development of mathema- tics in many respects (1, 119]. Hilbert‘s Sixteenth Problem (the second part) was stated as follows: Problem. To find the maximum number and to determine the relative position of limit cycles of the equation dy Qn(X, y) -= dx Pn(x, y)‘ where Pn and Qn are polynomials of real variables x, y with real coeffi- cients and not greater than n degree. The study of limit cycles is an interesting and very difficult problem of the qualitative theory of differential equations. This theory was origi- nated at the end of the nineteenth century in the works of two geniuses of the world science: of the Russian mathematician A. M. Lyapunov and of the French mathematician Henri Poincare. A. M. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154]. In tur | 出版日期 | Book 2003 | 關(guān)鍵詞 | differential equation; dynamical systems; dynamische Systeme; ecology; mathematics; mechanics; ordinary di | 版次 | 1 | doi | https://doi.org/10.1007/978-1-4419-9168-3 | isbn_softcover | 978-1-4613-4819-1 | isbn_ebook | 978-1-4419-9168-3 | copyright | Springer Science+Business Media New York 2003 |
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