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Recurrence to Shrinking Targets on Typical Self-Affine Fractals

Published online by Cambridge University Press:  15 February 2018

Henna Koivusalo*
Affiliation:
Faculty of Mathematics, University of Vienna, Oskar Morgensternplatz 1, 1090 Vienna, Austria ([email protected])
Felipe A. Ramírez
Affiliation:
Wesleyan University, Middletown, CT, USA ([email protected])
*
*Corresponding author.

Abstract

We explore the problem of finding the Hausdorff dimension of the set of points that recur to shrinking targets on a self-affine fractal. To be exact, we study the dimension of a certain related symbolic recurrence set. In many cases, this set is equivalent to the recurring set on the fractal.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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