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arXiv · 1404.2829

Convergence groups and semi conjugacy

Daniel Monclair
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Abstract

We study a simple problem that arises from the study of Lorentz surfaces and Anosov flows. For a non decreasing map of degree one $h:\mathbb{S}^1\to \mathbb{S}^1$, we are interested in groups of circle diffeomorphisms that act on the complement of the graph of $h$ in $\mathbb{S}^1\times \mathbb{S}^1$ by preserving a volume form. We show that such groups are semi conjugate to subgroups of $\mathrm{PSL}(2,\mathbb{R})$, and that when $h\in \mathrm{Homeo}(\mathbb{S}^1)$, we have a topological conjugacy. We also construct examples, where $h$ is not continuous, for which there is no such conjugacy.

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Daniel Monclair. 2014-04-10. Convergence groups and semi conjugacy. https://arxiv.org/abs/1404.2829

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