On non-Archimedean recurrence equations and their applications

Abstract

In the present paper we study stability of recurrence equations (which in particular case contain a 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 as well.