| 書目名稱 | Qualitative Theory of Planar Differential Systems | | 編輯 | Freddy Dumortier,Jaume Llibre,Joan C. Artés | | 視頻video | http://file.papertrans.cn/781/780187/780187.mp4 | | 概述 | Authors are among the leaders in their field and well-known expositors.Includes instruction manual and examples for the free software P4 (for numerical experiments on differential equations) available | | 叢書名稱 | Universitext | | 圖書封面 |  | | 描述 | Our aim is to study ordinary di?erential equations or simply di?erential s- tems in two real variables x ? = P(x,y), (0.1) y? = Q(x,y), r 2 where P and Q are C functions de?ned on an open subset U of R , with ? r=1,2,...,?,?.AsusualC standsforanalyticity.Weputspecialemphasis onto polynomial di?erential systems, i.e., on systems (0.1) where P and Q are polynomials. Instead of talking about the di?erential system (0.1), we frequently talk about its associated vector ?eld ? ? X = P(x,y) +Q(x,y) (0.2) ?x ?y 2 on U? R . This will enable a coordinate-free approach, which is typical in thetheoryofdynamicalsystems.Anotherwayexpressingthevector?eldisby writingitasX=(P,Q).Infact,wedonotdistinguishbetweenthedi?erential system (0.1) and its vector ?eld (0.2). Almost all the notions and results that we present for two-dimensional di?erential systems can be generalized to higher dimensions and manifolds; but our goal is not to present them in general, we want to develop all these notions and results in dimension 2. We would like this book to be a nice introduction to the qualitative theory of di?erential equations in the plane, providing simultaneously the major part of concepts and ideas for de | | 出版日期 | Textbook 2006 | | 關(guān)鍵詞 | Dynamical systems; ODE; ordinary differential equation; phase portrait; planar differential systems; qual | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-540-32902-2 | | isbn_softcover | 978-3-540-32893-3 | | isbn_ebook | 978-3-540-32902-2Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | Springer-Verlag Berlin Heidelberg 2006 |
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