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HOW POINTS ESCAPE TO INFINITY UNDER EXPONENTIAL MAPS

Published online by Cambridge University Press:  22 February 2006

BOGUSŁAWA KARPIŃSKA  and
MARIUSZ URBAŃSKI
BOGUSŁAWA KARPIŃSKA
Affiliation:
Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Plac Politechniki 1, Warsaw 00-661, Polandbkarpin@impan.gov.pl
MARIUSZ URBAŃSKI
Affiliation:
Department of Mathematics, University of North Texas, PO Box 311430, Denton, TX 76203-1430, USAurbanski@unt.edu
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Abstract

We investigate the finer fractal structure of the set of points escaping to infinity under iteration of an arbitrary exponential map. Providing exact formulas, we show how sensitively the Hausdorff dimension depends on the rate of growth of canonical Devaney–Krych codes.

Keywords

30D0537F1037F35
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 141 - 156
Copyright
The London Mathematical Society 2006

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