Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On questions of Fatou and Eremenko


Authors: P. J. Rippon and G. M. Stallard
Journal: Proc. Amer. Math. Soc. 133 (2005), 1119-1126
MSC (2000): Primary 37F10; Secondary 37F45
Published electronically: October 18, 2004
MathSciNet review: 2117213
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $f$ be a transcendental entire function and let $I(f)$ be the set of points whose iterates under $f$ tend to infinity. We show that $I(f)$ has at least one unbounded component. In the case that $f$ has a Baker wandering domain, we show that $I(f)$is a connected unbounded set.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37F10, 37F45

Retrieve articles in all journals with MSC (2000): 37F10, 37F45


Additional Information

P. J. Rippon
Affiliation: Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom
Email: p.j.rippon@open.ac.uk

G. M. Stallard
Affiliation: Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom
Email: g.m.stallard@open.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07805-0
PII: S 0002-9939(04)07805-0
Received by editor(s): April 4, 2003
Received by editor(s) in revised form: November 28, 2003
Published electronically: October 18, 2004
Dedicated: This paper is dedicated to the memory of Professor Noel Baker
Communicated by: Michael Handel
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.