Qualitative theory of planar differential systems / Freddy Dumortier, Jaume Llibre, Joan C. Artés.
"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,...,?,?.Asusual C standsforanalyticity.Weputspecialemphasis onto polynomial d...
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Ebook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
[2006]
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| Series: | Universitext.
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| Subjects: | |
| Online Access: | Springer eBooks Contributor biographical information |
| Summary: | "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,...,?,?.Asusual C 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 writingitas X=(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 developing a similar theory on more general surfaces and in higher dimensions. Except in very limited cases we do not deal with bifurcations, but focus on the study of individual systems."--Publisher's website. |
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| Physical Description: | 1 online resource (xvi, 298 pages) : illustrations. |
| Format: | Mode of access: World Wide Web. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 1281350931 3540329021 9781281350930 9783540329022 |