The M-set of λ exp(z)/z has infinite area-Reference-Cited by-同舟云学术

The M-set of λ exp(z)/z has infinite area

Published:2015-03 Issue: Volume:217 Page:133-159
ISSN:0027-7630
Container-title:Nagoya Mathematical Journal
language:en
Short-container-title:Nagoya Mathematical Journal

Author:

Zhan Guoping,Liao Liangwen

Abstract

AbstractIt is known that the Fatou set of the map exp(z)/z defined on the punctured plane ℂ* is empty. We consider the M-set of λ exp(z)/z consisting of all parameters λ for which the Fatou set of λexp(z)/z is empty. We prove that the M-set of λexp(z)/z has infinite area. In particular, the Hausdorff dimension of the M-set is 2. We also discuss the area of complement of the M-set.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference21 articles.

1. Area of non-escaping parameters of the sine family;Zhan;Houston J. Math.,2012

2. Devaney R. , Goldberg L. , and Hubbard J. H. , A dynamical approximation to the exponential map by polynomials, preprint, 1985.

3. Hausdorff dimension of the M-set of λexp(z);Qiu;Acta Math. Sinica,1994

4. Iterations of analytic functions in;Makienko;Dokl. Akad. Nauk,1987

5. Complex Dynamics

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