Dynamics of iterated function systems on the circle close to rotations
classification
🧮 math.DS
keywords
circlesystemsclosedynamicsfunctioniteratedrotationscantor
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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.
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