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Knaster-like continua and complex dynamics

Published online by Cambridge University Press:  19 September 2008

Robert L. Devaney
Robert L. Devaney
Affiliation:
Department of Mathematics, Boston University, Boston MA 02215, USA
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Abstract

In this paper we discuss the topology and dynamics of Eλ(z) = λez when λ is real and λ > 1/e. It is known that the Julia set of Eλ is the entire plane in this case. Our goal is to show that there are certain natural invariant subsets for Eλ which are topologically Knaster-like continua. Moreover, the dynamical behavior on these invariant sets is quite tame. We show that the only trivial kinds of α- and ω-limit sets are possible.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 4 , December 1993 , pp. 627 - 634
Copyright
Copyright © Cambridge University Press 1993

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