2025 : 9 : 29

Aliasghar Sarizadeh

Academic rank: Assistant Professor
ORCID:
Education: PhD.
ScopusId:
HIndex:
Faculty: Basic Science
Address:
Phone:

Research

Title
CHAOTIC ITERATED FUNCTION SYSTEMS
Type
JournalPaper
Keywords
iterated function systems, relations, transitivity, sensitivity, Devaney chaos
Year
2022
Journal ARCHIV DER MATHEMATIK
DOI
Researchers Aliasghar Sarizadeh

Abstract

The present work is concerned with chaotic iterated function systems, in more general case. In this regard, we consider a finite set of relations as the generators of our system. Then we study the behavior of some Kuratowski lower closed limit sets associated to every point of the phase space. In light of our observation, we propose a modified notation of chaos (in the sense of Devaney). In fact, this alteration is compatible with the original one. Also, it is shown that any chaotic IFS generated by relations is sensitive. Furthermore, we establish that the IFS generated by inverse relations of a chaotic IFS is either minimal or chaotic.