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Conformal Geometry and Dynamics

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Indecomposable continua in exponential dynamics


Authors: Robert L. Devaney and Xavier Jarque
Journal: Conform. Geom. Dyn. 6 (2002), 1-12
MSC (2000): Primary 37F10
DOI: https://doi.org/10.1090/S1088-4173-02-00080-2
Published electronically: January 16, 2002
MathSciNet review: 1882085
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Abstract: In this paper we prove the existence of uncountably many indecomposable continua in the dynamics of complex exponentials of the form $E_\lambda(z) = \lambda e^z$ with $\lambda > 1/e$. These continua contain points that share the same itinerary under iteration of $E_\lambda$. These itineraries are bounded but consist of blocks of $0$'s whose lengths increase, and hence these continua are never periodic.


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Additional Information

Robert L. Devaney
Affiliation: Department of Mathematics, Boston University, Boston, Massachusetts 02215
Email: bob@bu.edu

Xavier Jarque
Affiliation: University Autònoma de Barcelona, Barcelona (Bellaterra), Spain
Email: xavier.jarque@uab.es

DOI: https://doi.org/10.1090/S1088-4173-02-00080-2
Received by editor(s): August 29, 2001
Received by editor(s) in revised form: November 24, 2001
Published electronically: January 16, 2002
Article copyright: © Copyright 2002 American Mathematical Society