SYNDETICALLY TRANSITIVE AND SYNDETICALLY SENSITIVE ITERATED FUNCTION SYSTEMS E. REZAALI, F. H. GHANE * , AND H. EBADIZADEH Abstract . In this paper, we discuss several stronger forms of sensitivities for iterated func- tion 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 S 1 . We prove that each sensitive IFS acting on the circle S 1 generating by a finite family of circle homeomorphisms is strongly sensitive. However, to obtain syn- detical 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. 1. Introduction Sensitivity and chaos are two popular themes in dynamical systems. The sensitivity is widely understood as the central idea in chaos. The first formulate of sensitivity (as far as we know) was given by Guckenheimer on the study of interval maps, [7]. Then Liu and Wang [13] introduced some stronger versions of sensitivities, including thick sensitivity and thickly syndetical sensitivity. After that Wang, Yin and Yan [16] extended some of these results to semigroup actions. They introduced several stronger forms of sensitivities including thick sensitivity and thickly syndetical sensitivity. Then they presented some sufficient conditions for a dynamical system of semigroup actions to have these sensitivities. Sensitive systems were also studied by [1, 2, 3, 4, 6, 8, 11, 12]. In the present work we discuss some aspects of this concept in iterated function systems (IFSs). The paper is organized as follows: In Section 2, we recall some standard definitions about IFSs and their sensitivity properties. In section 3, we discuss several stronger forms 2010 Mathematics Subject Classification. 37B05; 37B10; 54H15; 54H20. Key words and phrases. iterated function systems, minimality, transitivity, sensitivity. * Corresponding author.