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.

14 pages

References in corpus (2)

• p-Adic Mathematical Physics
• On a recursive equation over $p$-adic field

Cited by in corpus (4)

• On $P$-adic Ising-Vannimenus model on an arbitrary order Cayley tree
• Renormalization method in $p$-adic $\lambda$-model on the Cayley tree
• Geometric location of periodic points of 2-ramified power series
• On unconventional limit sets of contractive functions on ${\mathbb{Z}}_p$