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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.

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