Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-08T08:03:05.954Z Has data issue: false hasContentIssue false
  • English
  • Français

Constructing ergodic exponential maps with dense post-singular orbits

Published online by Cambridge University Press:  03 February 2009

XIUMEI WANG  and
GAOFEI ZHANG
XIUMEI WANG
Affiliation:
Department of Computer Science and Information Technology, JiangSu Teachers University of Technology, Changzhou, 213001, People’s Republic of China (email: wxmei@jstu.edu.cn)
GAOFEI ZHANG
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China (email: zhanggf@hotmail.com)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We construct ergodic exponential maps fλ(z)=λez such that the forward orbit of the origin is dense in $\Bbb C$.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 1 , February 2010 , pp. 309 - 316
Copyright
Copyright © Cambridge University Press 2009

References

[1]Baker, I. N. and Rippon, P. J.. Iteration of exponential functions. Ann. Acad. Sci. Fenn. Ser. A. I Math. 9 (1984), 49–77.CrossRefGoogle Scholar
[2]Eremenko, A. and Lyubich, M.. Dynamical properties of some classes of entire functions. Ann. Inst. Fourier 42 (1922), 989–1020.Google Scholar
[3]Keen, L. and Kotus, J.. Ergodicity of some classes of meromorphic functions. Ann. Acad. Sci. Fenn. Math. 24 (1999), 133–145.Google Scholar
[4]Rees, M.. Ergodic rational maps with dense critical point forward orbit. Ergod. Th. & Dynam. Sys. 4 (1984), 311–322.Google Scholar