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

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
Keywords Difference equations  asymptotics  stability  rivers  nonstandard analysis  change of scale
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DOI 10.1007/s11813-008-0006-0
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Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..
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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