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On the dimension of points which escape to infinity at given rate under exponential iteration

Part of: Entire and meromorphic functions, and related topics Classical measure theory Complex dynamical systems

Published online by Cambridge University Press:  29 March 2021

KRZYSZTOF BARAŃSKI  and
BOGUSŁAWA KARPIŃSKA
KRZYSZTOF BARAŃSKI
Affiliation:
Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097Warszawa, Poland (e-mail: baranski@mimuw.edu.pl)
BOGUSŁAWA KARPIŃSKA*
Affiliation:
Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-661Warszawa, Poland
*
e-mail: bkarpin@mini.pw.edu.pl
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Abstract

We prove a number of results concerning the Hausdorff and packing dimension of sets of points which escape (at least in average) to infinity at a given rate under non-autonomous iteration of exponential maps. In particular, we generalize the results proved by Sixsmith in 2016 and answer his question on annular itineraries for exponential maps.

Keywords

exponential mapiterationHausdorff dimensionescaping set

MSC classification

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions 37F35: Conformal densities and Hausdorff dimension 30D05: Functional equations in the complex domain, iteration and composition of analytic functions 30D15: Special classes of entire functions and growth estimates
Secondary: 28A78: Hausdorff and packing measures 28A80: Fractals
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 5 , May 2022 , pp. 1591 - 1623
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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