Asymptotics of families of solutions of nonlinear difference equations |
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Authors: | Imme P van den Berg |
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Affiliation: | 1. Departamento de Matemática, Universidade de évora, Colégio Luís Verney, Rua Rom?o Ramalho 59, 7000-671, évora, Portugal
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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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Keywords: | Difference equations asymptotics stability rivers nonstandard analysis change of scale |
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