ON A GENERALIZED SELF-SIMILARITY IN THE p-ADIC FIELD

Abstract

In the present paper, we introduce a new set which defines a generalized self-similar set for contractive functions [Formula: see text] on the unit ball [Formula: see text] of [Formula: see text]-adic numbers. This set is called unconventional limit set. 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.