References of "Ergodic Theory and Dynamical Systems"
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See detailConvergence groups and semiconjugacy
Monclair, Daniel UL

in Ergodic Theory and Dynamical Systems (2015), First view(1469-4417), 1-26

We study a problem that arises from the study of Lorentz surfaces and Anosov flows. For a non-decreasing map of degree one h:S^1->S^1, we are interested in groups of circle diffeomorphisms that act on the ... [more ▼]

We study a problem that arises from the study of Lorentz surfaces and Anosov flows. For a non-decreasing map of degree one h:S^1->S^1, we are interested in groups of circle diffeomorphisms that act on the complement of the graph of h in S1^×S^1 by preserving a volume form. We show that such groups are semiconjugate to subgroups of PSL(2,R) and that, when h∈Homeo(S^1), we have a topological conjugacy. We also construct examples where h is not continuous, for which there is no such conjugacy. [less ▲]

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