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Bulletin of the London Mathematical Society Advance Access originally published online on August 22, 2007
Bulletin of the London Mathematical Society 2007 39(5):724-730; doi:10.1112/blms/bdm055
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© 2007 London Mathematical Society

Quasi-symmetric conjugacy of Blaschke products on the unit circle

Carsten Lunde Petersen

IMFUFA
NSM Roskilde University
Postbox 260
DK-4000 Roskilde
Denmark

Received 31 August 2006. Revision received 4 January 2007.

Let B be a Blaschke product for which the restriction to the unit circle S1 is a degree d > 1 covering. We prove that B is quasi-symmetrically conjugate to z {rightarrowtail} zd on S1, if all its periodic points in S1 are repelling and if S1 does not intersect the {omega}-limit set of any recurrent critical point for B.

2000 Mathematics Subject Classification 37E10, 37F10 (primary), 37F15 (secondary).


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