Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Structural instability of $\textrm {exp}(z)$


Author: Robert L. Devaney
Journal: Proc. Amer. Math. Soc. 94 (1985), 545-548
MSC: Primary 58F12; Secondary 30D05, 58F10
DOI: https://doi.org/10.1090/S0002-9939-1985-0787910-2
MathSciNet review: 787910
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The entire function $\operatorname {exp}\left ( z \right )$ has a Julia set equal to the whole plane. We show that there are complex $\lambda$’s near 1 such that $\lambda {e^z}$ has an attracting periodic orbit. Hence ${e^z}$ is not structurally stable.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F12, 30D05, 58F10

Retrieve articles in all journals with MSC: 58F12, 30D05, 58F10


Additional Information

Keywords: Exponential map, Julia set, structural stability
Article copyright: © Copyright 1985 American Mathematical Society