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On iterates of ez

Published online by Cambridge University Press:  19 September 2008

Michał Misiurewicz
Michał Misiurewicz*
Affiliation:
Department of Mathematics, University of Maryland, USA; and Mathematics Institute, Warsaw University, Poland
*
†Dr Michal Misiurewicz, Mathematics Institute, Warsaw University, PKiNIXp, 00-901 Warszawa, Poland.
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Abstract

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It is proved that for the map f: ℂ → ℂ given by f(z) = ez, the family is not normal at any point. In particular, f is topologically transitive.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 1 , March 1981 , pp. 103 - 106
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

[1]Baker, I. N.. Limit functions and sets of non-normality in iteration theory. Ann. Acad. Sei. Fennicae, Ser. A.I. Math. 467 (1970).Google Scholar
[2]Fatou, P.. Sur l'itération des fonctions transcendantes entières. Acta Math. 47 (1926), 337–370.CrossRefGoogle Scholar
[3]Töpfer, H.. Uber die Iteration der ganzen transzendenten Funktionen, insbesondere von sin and cos. Math. Ann. 117 (1940), 65–84.CrossRefGoogle Scholar