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A Compactification of the Space of Expanding Maps on the Circle

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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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Authors and Affiliations

  1. Mathematics Department, Harvard University, 1 Oxford St, Cambridge, MA, 02138-2901, USA

    Curtis T. McMullen

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  1. Curtis T. McMullen
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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

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