Přes Balíkovnu doručujeme za 49 Kč

Knihobot
Knihu momentálně nemáme skladem

Qualitative theory of planar differential systems

Autoři

Více o knize

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.

Parametry

ISBN
9783540328933
Nakladatelství
Springer

Kategorie

Varianta knihy

2006, měkká

Nákup knihy

Jakmile ji vyčmucháme, pošleme vám e-mail.