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arXiv · 1303.2521

Dynamics of iterated function systems on the circle close to rotations

Pablo G. Barrientos·Artem Raibekas
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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.

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Pablo G. Barrientos, Artem Raibekas. 2015-07-16. Dynamics of iterated function systems on the circle close to rotations. https://doi.org/10.1017/etds.2013.112

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