{"product_id":"qualitative-theory-of-planar-differential-systems-von-joan-c-artes-freddy-dumortier-jaume-llibre","title":"Qualitative Theory of Planar Differential Systems","description":"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 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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783540328933\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783540328933","offer_id":39434702651485,"sku":"9783540328933","price":80.24,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/5068454c-4983-4c99-a682-292f1071cfa9.jpg?v=1772171936","url":"https:\/\/shop.autorenwelt.de\/products\/qualitative-theory-of-planar-differential-systems-von-joan-c-artes-freddy-dumortier-jaume-llibre","provider":"Autorenwelt Shop","version":"1.0","type":"link"}