Dimension properties of the boundaries of exponential basins

Details Dimension properties of the boundaries of exponential basins Dimension properties of the boundaries of exponential basins

2009-02-06

arxiv.org/abs/0902.1065v1

Bull. Lond. Math. Soc. 42 (2010), 210-220

Mathematics

Dynamical Systems

13 pages, 1 figure

Scientific paper

10.1112/blms/bdp105

We prove that the boundary of a component $U$ of the basin of an attracting periodic cycle (of period greater than 1) for an exponential map on the complex plane has Hausdorff dimension greater than 1 and less than 2. Moreover, the set of points in the boundary of $U$ which do not escape to infinity has Hausdorff dimension (in fact: hyperbolic dimension) greater than 1, while the set of points in the boundary of $U$ which escape to infinity has Hausdorff dimension 1.

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