Asymptotics of families of solutions of nonlinear difference equations

Logic and Analysis 1 (2):153-185 (2008)
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Abstract

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given

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10.1007/s11813-008-0006-0

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Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
Internal Set Theory: A New Approach to Nonstandard Analysis.Edward Nelson - 1977 - Journal of Symbolic Logic 48 (4):1203-1204.
Extended use of IST.I. P. Van den Berg - 1992 - Annals of Pure and Applied Logic 58 (1):73-92.

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