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Convergence of solutions ofPSL(2, R)-recurrences with parabolic limit

Authors
Journal
Indagationes Mathematicae
0019-3577
Publisher
Elsevier
Publication Date
Volume
5
Issue
1
Identifiers
DOI: 10.1016/0019-3577(94)90035-3

Abstract

Abstract The aim of this paper is the investigation of the convergence of the solutions { Z n } of a sequence of Möbius-transformations with parabolic limit. It is shown that either lim n→∞ Z n exists for all solutions or it exists for none of them. In the first part of the paper a description for the behaviour of solutions in the boundary region (between converging and non-converging type) is given with the aid of a certain class of renormalizations. A generalization of this idea is used in the second part to derive a necessary and sufficient condition for convergence in terms of the coefficients of the Möbius-transformations. Lastly, an application to second-order linear recurrences is given.

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