Conformal Geometry and Dynamics

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ISSN 1088-4173

Indecomposable continua in exponential dynamics

Author(s): Robert L. Devaney; Xavier Jarque
Journal: Conform. Geom. Dyn. 6 (2002), 1-12.
MSC (2000): Primary 37F10
Posted: 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 's whose lengths increase, and hence these continua are never periodic.

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