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Journal of the London Mathematical Society 2006 73(1):141-156; doi:10.1112/S0024610705022465
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© The London Mathematical Society

How Points Escape to Infinity Under Exponential Maps

Boguslawa Karpinska and Mariusz Urbanski

Faculty of Mathematics and Information Sciences, Warsaw University of Technology Plac Politechniki 1, Warsaw 00-661, Poland bkarpin{at}impan.gov.pl
Department of Mathematics, University of North Texas PO Box 311430, Denton, TX 76203-1430, USA urbanski{at}unt.edu

Received 12 October 2004. Revision received 8 March 2005.

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.


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