1. Non-locally discrete actions on the circle with at most N fixed points.
- Author
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Bonatti, Christian, Carnevale, João, and Triestino, Michele
- Abstract
A subgroup of Homeo + (S 1) is Möbius-like if every element is conjugate to an element of PSL (2 , R) . In general, a Möbius-like subgroup of Homeo + (S 1) is not necessarily (semi-)conjugate to a subgroup of PSL (2 , R) , as discovered by Kovačević (Trans Am Math Soc 351:4823–4835, 1999). Here we determine simple dynamical criteria for the existence of such a (semi-)conjugacy. We show that Möbius-like subgroups of Homeo + (S 1) which are elementary (namely, preserving a Borel probability measure), are semi-conjugate to subgroups of PSL (2 , R) . On the other hand, we provide an example of elementary subgroup of Diff + ∞ (S 1) satisfying that every non-trivial element fixes at most 2 points, which is not isomorphic to any subgroup of PSL (2 , 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 PSL (2 , R) . [ABSTRACT FROM AUTHOR]
- Published
- 2024
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