ON A GENERALIZED SELF-SIMILARITY IN THE p-ADIC FIELD
Farrukh MukhamedovDepartment of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P. O. Box, 141, 25710 Kuantan, Pahang, MalaysiaOtabek KhakimovInstitute of Mathematics, National University of Uzbekistan, 29 Do’rmon Yo’li str., 100125, Tashkent, Uzbekistan
ABI
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.