On unconventional limit sets of contractive functions on ${\mathbb{Z}}_p$

Abstract

In the present paper, we are going to study metric properties of unconventional limit set of a semigroup $G$ generated by contractive functions $\{f_i{\}}_{i=1}^N$ on the unit ball ${\mathbb{Z}}_p$ of $p$-adic numbers. Namely, we prove that the unconventional limit set is compact, perfect and uniformly disconnected. Moreover, we provide an example of two contractions for which the corresponding unconventional limiting set is quasi-symmetrically equivalent to the symbolic Cantor set.

14 pages

References in corpus (1)

• On non-Archimedean recurrence equations and their applications