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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