Open Access
Article
Syndetically transitive and syndetically sensitive Iterated Function Systems
E. Rezaaliesmaeel.rezaali@gmail.comDepartment of mathematicsFerdowsi University of Mashhad (FUM)Mashhad, 1159-91775, IranView full profile → , *F. H. GhaneCorresponding authorghane@math.um.ac.irDepartment of mathematicsFerdowsi University of Mashhad (FUM)Mashhad, 1159-91775, IranView full profile → , H. Ebadizadehebadizadeh.h@gmail.comYoung Researchers and Elite ClubIslamic Azad UniversityIslamshahr Branch, Islamshar, IranView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 28 Jul 2017
- Accepted:
- 17 Nov 2017
- Published Online:
- 30 Oct 2018
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2018.1436273
- Pages:
- 129–137
Abstract
In this paper, we discuss several stronger forms of sensitivities for iterated function systems (IFSs), such as strong sensitivity and syndetical sensitivity, and obtain some sufficient conditions for an IFS to have such sensitivities. We pay special attention to IFSs acting on the circle S1. We prove that each sensitive IFS acting on the circle S1 generating by a finite family of circle homeomorphisms is strongly sensitive. However, to obtain syndetical sensitivity, we impose some extra conditions on the IFS. Finally, we study sensitivity properties for syndetical transitive IFSs. We show that each syndetically transitive IFS is topologically ergodic.
Keywords
Subject Classifications
37B0537B1054H1554H20
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