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On the measurable dynamics of z → ez

Published online by Cambridge University Press:  19 September 2008

Etienne Ghys ,
Lisa R. Goldberg  and
Dennis P. Sullivan
Etienne Ghys
Affiliation:
Université des Sciences de LilleI 59655- Villeneuve d'Asq Cedex, France
Lisa R. Goldberg
Affiliation:
CUNY, 33 W 42nd St., New York, NY 10036, USA
Dennis P. Sullivan
Affiliation:
CUNY and IHES, 35, route de Chartres, 91 440-Bures sur Yvette, France
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Abstract

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We study the measure theoretic properties of the complex exponential map E(z) = ez.An particular, we show that the equivalence relation generated by E is recurrent and that E has no quasi-conformal deformations. This enables us to give some information concerning Devaney's semi-conjugacy between E and the shift map on sequences of integers.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 3 , September 1985 , pp. 329 - 335
Copyright
Copyright © Cambridge University Press 1985

References

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