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Bulletin of the London Mathematical Society 1983 15(4):343-348; doi:10.1112/blms/15.4.343
© 1983 by London Mathematical Society
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© Oxford University Press

On Finite Blaschke Products whose Restrictions to the unit circle are Exact Endomorphisms

N. F. G. Martin

Department of Mathematics, Math/Astronomy Building, University of Virginia Charlottesville, Virginia 22903, U.S.A.

An easily checked sufficient condition is given for the restriction of a finite Blaschke product to the unit circle to be an exact endomorphism. A formula for the entropy of such restrictions with respect to the unique finite invariant measure equivalent to Lebesgue measure is given and it is shown that if such a restriction has maximal entropy then it is conformally equivalent to the product of a rotation and a power.


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