Rotational Entropy of an Annular Iterated Functions System. Issue 2 (3rd July 2021)

• Record Type: Journal Article
• Authors: Rezaei, Fatemeh; Nia, Mehdi Fatehi
• Is Part Of: Journal of dynamical systems and geometric theories. Volume 19:Issue 2(2021)
• Page Start: 189
• Page End: 202
• Publication Date: 2021-07-03
• Subjects: 54H20 -- 37B55; Rotational entropy -- Spanning set -- Separating set -- Topological invariant -- Non-wandering set; Differentiable dynamical systems -- Periodicals; Geometry -- Periodicals; Differentiable dynamical systems; Geometry; Periodicals; 515.39
• DOI: 10.1080/1726037X.2021.2009199
• Languages: English
• ISSNs: 1726-037X

Abstract

Abstract: In this article, we consider an iterated functions system (IFS) whose functions are homeomorphisms on an annulus. We define rotational spanning and separating sets for the IFS and then provide two definitions for the rotational entropy of the IFS. We show that in the IFSs, the rotational entropy is a topological invariant. We prove that the rotational entropy of an annular IFS is equal to the rotational entropy on its non-wandering set for sequences of functions with a specific condition.