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VOL. 53 | 2009 Dissipative delay endomorphisms and asymptotic equivalence
Christian Pötzsche

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose

Abstract

Using an invariant manifold theorem we demonstrate that the dynamics of nonautonomous dissipative delayed difference equations (with delay $M$) is asymptotically equivalent to the long-term behavior of an $N$-dimensional first order difference equation (with $N \leq M)$ – assumed the nonlinearity is small Lipschitzian on the absorbing set. As consequence we obtain a result of Kirchgraber that multi-step methods for the numerical solution of ordinary differential equations are essentially one-step methods, and generalize it to varying step-sizes.

Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1182.39009
MathSciNet: MR2582422

Digital Object Identifier: 10.2969/aspm/05310237

Subjects:
Primary: 37D10, 39A11, 65L06

Rights: Copyright © 2009 Mathematical Society of Japan

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