Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Advances in Discrete Dynamical Systems, S. Elaydi, K. Nishimura, M. Shishikura and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 237 - 259
Dissipative delay endomorphisms and asymptotic equivalence
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.
Received: 30 October 2006
First available in Project Euclid: 28 November 2018
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Pötzsche, Christian. Dissipative delay endomorphisms and asymptotic equivalence. Advances in Discrete Dynamical Systems, 237--259, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05310237. https://projecteuclid.org/euclid.aspm/1543447658