A Compactification of the Space of Expanding Maps on the Circle
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- McMullen, C.T. GAFA Geom. funct. anal. (2009) 18: 2101. doi:10.1007/s00039-009-0709-8
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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.