Adding machine maps and minimal sets for iterated function systems

Various shadowing properties and their equivalent for expansive iterated function systems

“…In the other hand, iterated function systems( IFS), are used for the construction of deterministic fractals and have found numerous applications, in particular to image compression and image processing [2]. Important notions in dynamics like attractors, minimality, transitivity, and shadowing can be extended to IFS (see [3,4,[7][8][9]). The authors defined the shadowing property for a parameterized iterated function system and prove that if a parameterized IFS is uniformly expanding ( or contracting), then it has the shadowing property [9].…”

Chaos and Shadowing in General Systems

“…Shadowing and ergodic properties in discrete dynamical systems have received increasing attention in recent years [4][5][6][7]. Many authors investigated the relation between shadowing properties and other ergodic properties such as mixing and transitivity [10,12,14].…”