C2-Iterated Function Systems on the Circle and Symbolic Blender-like
Iterated Function Systems | Blender | Skew-Products
We study the dynamics of an iterated function system (IFS) given by a pair of C^2 Morse-Smale diffeomorphisms on the circle, but with the extra assumption that the maps are C^2-close to the identity. For this systems it will be proven the existence of minimal sets with non-empty interior. When both maps have hyperbolic fixed points it is possible to give a complete topological description of the dynamics and simple combinatorial criteria is given to obtain minimality of the whole circle. We also study the relationships between minimal sets with non-empty interior for iterated function systems on one hand and symbolic blenders and skew-products on the other.