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On ergodic properties of restrictions of inner functions

Published online by Cambridge University Press:  19 September 2008

N.F.G. Martin
N.F.G. Martin
Affiliation:
Department of Mathematics, Math-Astronomy Building, University of Virginia, Charlottesville, VA 22903, USA
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Abstract

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We consider inner functions on the unit disk which have a finite number of singularities on the unit circle. The restriction of such functions to the circle are maps onto the circle. We give sufficient conditions that these restrictions are exact endomorphisms whose natural extensions are Bernoulli and that the entropy is given by Rohlin's formula, We also give the entropy in closed form if ƒ' is in the Nevalinna class N. An example is considered. In the last section we show that if two restrictions are metrically isomorphic, they are diffeomorphic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 1 , March 1989 , pp. 137 - 151
Copyright
Copyright © Cambridge University Press 1989

References

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