| 书目名称 | Global Bifurcation Theory and Hilbert’s Sixteenth Problem | | 编辑 | Valery A. Gaiko | | 视频video | | | 丛书名称 | Mathematics and Its Applications | | 图书封面 |  | | 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 | | 关键词 | 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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发表于 2025-3-21 20:09:21
