On the measurable dynamics of z → ez-Reference-Cited by-同舟云学术

On the measurable dynamics of z → ez

Published:1985-09 Issue:3 Volume:5 Page:329-335
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

Ghys Etienne,Goldberg Lisa R.,Sullivan Dennis P.

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference14 articles.

1. [5] Devaney R. . Structural instability of Exp(z). To appear.

2. Mémoire sur les equations fonctionnelles;Fatou;B.S.M.F.,1919

3. [9] Halmos P. . Ergodic Theory.

4. Quasiconformal Mappings in the Plane

5. Itération des applications fonctionelles;Julia;J. Math. Pures et Appl.,1918

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Julia sets of Zorich maps;Ergodic Theory and Dynamical Systems;2021-11-15

2. Computer research of the holomorphic dynamics of exponential and linear-exponential maps;Computer Research and Modeling;2018-08

3. Experimental research of iterated dynamics for the complex exponentials with linear term;Journal of Physics: Conference Series;2018-03

4. Most of the Maps near the Exponential are Hyperbolic;Nagoya Mathematical Journal;2008

5. Iteration of meromorphic functions;Bulletin of the American Mathematical Society;1993