Geometric and Functional Analysis

, Volume 18, Issue 6, pp 2101–2119

A Compactification of the Space of Expanding Maps on the Circle


  • Curtis T. McMullen
    • Mathematics DepartmentHarvard University

DOI: 10.1007/s00039-009-0709-8

Cite this article as:
McMullen, C.T. GAFA Geom. funct. anal. (2009) 18: 2101. doi:10.1007/s00039-009-0709-8


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.

Keywords and phrases:

Expanding mapsBlaschke productsinvariant measurescomplex dynamicsTeichmüller theory

AMS Mathematics Subject Classification:

Primary 37F30Secondary 37A05, 37E10

Copyright information

© Birkhäuser Verlag, Basel 2009