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On non-Archimedean recurrence equations and their applications. (English) Zbl 1303.39011
Summary: In the present paper we study stability of recurrence equations (which in particular case contain dynamics of rational functions) generated by contractive functions defined on an arbitrary non-Archimedean algebra. Moreover, multirecurrence equations are considered. We also investigate reverse recurrence equations which have application in the study of \(p\)-adic Gibbs measures. Note that our results also provide the existence of unique solutions of nonlinear functional equations. We should stress that the non-Archimedeanity of the algebra is essentially used, therefore, the methods applied in the present paper are not valid in the Archimedean setting.

MSC:
39A30 Stability theory for difference equations
39A10 Additive difference equations
39B82 Stability, separation, extension, and related topics for functional equations
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