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Knobbly but nice

Part of: Complex dynamical systems

Published online by Cambridge University Press:  08 May 2020

NEIL DOBBS Open the ORCID record for NEIL DOBBS [Opens in a new window]
NEIL DOBBS*
Affiliation:
School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 14, Ireland email neil.dobbs@ucd.ie
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Abstract

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Our main result states that, under an exponential map whose Julia set is the whole complex plane, on each piecewise smooth Jordan curve there is a point whose orbit is dense. This has consequences for the boundaries of nice sets, used in induction methods to study ergodic and geometric properties of the dynamics.

Keywords

low-dimensional dynamicscomplex dynamicstranscendentalexponential

MSC classification

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 7 , July 2021 , pp. 2016 - 2022
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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