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Dynamics of iterated function systems on the circle close to rotations

Published online by Cambridge University Press:  23 April 2014

PABLO G. BARRIENTOS  and
ARTEM RAIBEKAS
PABLO G. BARRIENTOS
Affiliation:
Departamento de Matemática PUC-Rio, Marquês de São Vicente 225, Gávea, Rio de Janeiro 225453-900, Brazil email [email protected]
ARTEM RAIBEKAS
Affiliation:
Instituto de Matemática e Estatística, UFF Rua Mário Santos Braga s/n–Campus Valonguinhos, Niterói, Brazil email [email protected]
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Abstract

We study the dynamics of iterated function systems generated by a pair of circle diffeomorphisms close to rotations in the $C^{1+\text{bv}}$-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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 5 , August 2015 , pp. 1345 - 1368
Copyright
© Cambridge University Press, 2014 

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