Ordinary Differential Equations: Second EditionSIAM, 01 հնվ, 1982 թ. - 632 էջ Ordinary Differential Equations covers the fundamentals of the theory of ordinary differential equations (ODEs), including an extensive discussion of the integration of differential inequalities, on which this theory relies heavily. In addition to these results, the text illustrates techniques involving simple topological arguments, fixed point theorems, and basic facts of functional analysis. Unlike many texts, which supply only the standard simplified theorems, this book presents the basic theory of ODEs in a general way. This SIAM reissue of the 1982 second edition covers invariant manifolds, perturbations, and dichotomies, making the text relevant to current studies of geometrical theory of differential equations and dynamical systems. In particular, Ordinary Differential Equations includes the proof of the Hartman-Grobman theorem on the equivalence of a nonlinear to a linear flow in the neighborhood of a hyperbolic stationary point, as well as theorems on smooth equivalences, the smoothness of invariant manifolds, and the reduction of problems on ODEs to those on "maps" (Poincar?). Audience: readers should have knowledge of matrix theory and the ability to deal with functions of real variables. |
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CL38_backmatter | 557 |
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addition analogue analytic applicable arbitrary arcs argument assertion Assume assumption asymptotic Banach space boundary bounded called Chapter class C1 clear closed complete Consequently Consider constant contains continuous function convergent Corollary corresponding curve defined definite denote depend derivative determined dichotomy differential equations eigenvalues elements equivalent Exercise exists exterior derivative fact Figure first fixed follows function given gives Hartman Hence holds implies inequality integral interval Jordan least Lemma Let u(t limit linear Math matrix norm Note obtain partial particular periodic positive proof proof of Theorem proves real-valued relation Remark replaced respect result satisfies satisfying sequence Show solution solution u(t space Suppose Theorem Theorem 6.1 theory uniformly variables vector zeros