Dynamics of iterated function systems on the circle close to rotations

Abstract

We study the dynamics of iteration function systems generated by a pair of circle diffeomorphisms close to rotations in the $C^{1+\mathrm{bv}}$-topology. We characterize the obstruction to minimality and describe the limit set. In particular, there are no invariant minimal Cantor sets, which can be seen as a Denjoy/Duminy type theorem for iterated systems on the circle.

References in corpus (3)

• Symbolic blender-horseshoes and applications
• On the minimality of semigroup actions on the interval which are $C^1$-close to the identity
• Some examples of minimal Cantor set for IFSs with overlap

Cited by in corpus (4)

• On the chaos game of Iterated Function Systems
• Expanding actions: minimality and ergodicity
• Density of fiberwise orbits in minimal iterated function systems on the circle
• Stable local dynamics: expansion, quasi-conformality and ergodicity