Indecomposable continua in exponential dynamics

Devaney, Robert; Jarque, Xavier

doi:10.1090/S1088-4173-02-00080-2

Indecomposable continua in exponential dynamics
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by Robert L. Devaney and Xavier Jarque

Conform. Geom. Dyn. 6 (2002), 1-12

DOI: https://doi.org/10.1090/S1088-4173-02-00080-2

Published electronically: January 16, 2002

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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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