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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Indecomposable continua in exponential dynamics
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by Robert L. Devaney and Xavier Jarque PDF
Conform. Geom. Dyn. 6 (2002), 1-12 Request permission

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
  • MR Author ID: 57240
  • Email: bob@bu.edu
  • Xavier Jarque
  • Affiliation: University Autònoma de Barcelona, Barcelona (Bellaterra), Spain
  • Email: xavier.jarque@uab.es
  • Received by editor(s): August 29, 2001
  • Received by editor(s) in revised form: November 24, 2001
  • Published electronically: January 16, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 6 (2002), 1-12
  • MSC (2000): Primary 37F10
  • DOI: https://doi.org/10.1090/S1088-4173-02-00080-2
  • MathSciNet review: 1882085