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arXiv · 1407.4638

Dimensions of slowly escaping sets and annular itineraries for exponential functions

D. J. Sixsmith
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Abstract

We study the iteration of functions in the exponential family. We construct a number of sets, consisting of points which escape to infinity `slowly', and which have Hausdorff dimension equal to 1. We prove these results by using the idea of an annular itinerary. In the case of a general transcendental entire function we show that one of these sets, the uniformly slowly escaping set, has strong dynamical properties and we give a necessary and sufficient condition for this set to be non-empty.

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D. J. Sixsmith. 2014-07-17. Dimensions of slowly escaping sets and annular itineraries for exponential functions. https://doi.org/10.1017/etds.2015.7

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