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- W4381586592 abstract "A subgroup of $mathrm{Homeo}_+(mathbb{S}^1)$ is Mobius-like if every element is conjugate to an element of $mathrm{PSL}(2,mathbb{R})$. In general, a Mobius-like subgroup of $mathrm{Homeo}_+(mathbb{S}^1)$ is not necessarily (semi-)conjugate to a subgroup of $mathrm{PSL}(2,mathbb{R})$, as discovered by N. Kovav{c}evi'{c} [Trans. Amer. Math. Soc. 351 (1999), 4823-4835]. Here we determine simple dynamical criteria for the existence of such a (semi-)conjugacy. We show that Mobius-like subgroups of $mathrm{Homeo}_+(mathbb{S}^1)$ which are elementary (namely, preserving a Borel probability measure), are semi-conjugate to subgroups of $mathrm{PSL}(2,mathbb{R})$. On the other hand, we provide an example of elementary subgroup of $mathrm{Diff}^infty_+(mathbb{S}^1)$ satisfying that every non-trivial element fixes at most 2 points, which is not isomorphic to any subgroup of $mathrm{PSL}(2,mathbb{R})$. Finally, we show that non-elementary, non-locally discrete subgroups acting with at most $N$ fixed points are conjugate to a dense subgroup of some finite central extension of $mathrm{PSL}(2,mathbb{R})$." @default.
- W4381586592 created "2023-06-22" @default.
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- W4381586592 date "2023-06-20" @default.
- W4381586592 modified "2023-10-18" @default.
- W4381586592 title "Non-locally discrete actions on the circle with at most $N$ fixed points" @default.
- W4381586592 doi "https://doi.org/10.48550/arxiv.2306.11517" @default.
- W4381586592 hasPublicationYear "2023" @default.
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