Dynamics of iterated function systems on the circle close to rotations
Pablo G. Barrientos, Artem Raibekas
TL;DR
This paper investigates the behavior of iterated function systems on the circle near rotations, identifying conditions for minimality and describing their limit sets, extending classical results to systems rather than single maps.
Contribution
It provides a characterization of obstructions to minimality and describes limit sets for circle diffeomorphisms close to rotations, akin to a Denjoy/Duminy theorem for systems.
Findings
No invariant minimal Cantor sets exist for systems close to rotations
Characterization of obstructions to minimality in iterated systems
Description of the limit set structure for these systems
Abstract
We study the dynamics of iteration function systems generated by a pair of circle diffeomorphisms close to rotations in the -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.
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