Publication: A Compactification of the Space of Expanding Maps on the Circle
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Date
2009
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Springer Verlag
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McMullen, Curtis T. 2009. A compactification of the space of expanding maps on the circle. Geometric and Functional Analysis 18(6): 2101-2119.
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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Keywords
expanding maps, Blaschke products, invariant measures, complex dynamics, Teichmüller theory
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