Abstract.
We show the space of expanding Blaschke products on S1 is compactified by a sphere of invariant measures, reminiscent of the sphere of geodesic currents for a hyperbolic surface. More generally, we develop a dynamical compactification for the Teichmüller space of all measure preserving topological covering maps of S1.
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Received: July 2007, Revision: March 2008, Accepted: March 2008
Research supported in part by the NSF.
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McMullen, C.T. A Compactification of the Space of Expanding Maps on the Circle. GAFA Geom. funct. anal. 18, 2101–2119 (2009). https://doi.org/10.1007/s00039-009-0709-8
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DOI: https://doi.org/10.1007/s00039-009-0709-8