, Volume 18, Issue 6, pp 2101-2119
Date: 11 Feb 2009

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 S 1 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 S 1.

Received: July 2007, Revision: March 2008, Accepted: March 2008
Research supported in part by the NSF.