Open Access
Research Article
On Equicontinuity, Transitivity and Distality of Iterated Function Systems
*Thiyam Thadoi DeviCorresponding authorthadoithiyam@manipuruniv.ac.inDepartment Of MathematicsManipur UniversityCanchipur, Imphal, 795003, ManipurView full profile → , Khundrakpam Binod Mangangkhubim@manipuruniv.ac.inDepartment Of MathematicsManipur UniversityCanchipur, Imphal, 795003, ManipurView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 22 Jul 2020
- Accepted:
- 14 Aug 2020
- Published Online:
- 07 Jan 2021
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- 1726037X.2020.1847766
- Pages:
- 223–239
Abstract
In this paper, equicontinuity, transitivity, minimality, sensitivity, and distality of iterated function systems(IFS) have been discussed. The equicontinuity, almost equicontinuity, and distality of an IFS have been defined and some relevant results have been introduced and proved. The transitivity, minimality, and sensitivity of an IFS F have been investigated when each of the constituent maps f has these properties and vice versa. It has been found that the IFS has these properties if at least one of the constituent maps f has these properties but the converse statements are not true. We give counterexamples to support that the converse statements are not true. It has also been shown that an IFS F is distal if and only if the constituent maps f are distal.
Keywords
Subject Classifications
54H2037B0526A18
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