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Recurrence to Shrinking Targets on Typical Self-Affine Fractals

Part of: Classical measure theory Smooth dynamical systems: general theory

Published online by Cambridge University Press:  15 February 2018

Henna Koivusalo  and
Felipe A. Ramírez
Henna Koivusalo*
Affiliation:
Faculty of Mathematics, University of Vienna, Oskar Morgensternplatz 1, 1090 Vienna, Austria (henna.koivusalo@univie.ac.at)
Felipe A. Ramírez
Affiliation:
Wesleyan University, Middletown, CT, USA (framirez@wesleyan.edu)
*
*Corresponding author.
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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.

Keywords

self-affine setsshrinking targetHausdorff dimension

MSC classification

Primary: 37C45: Dimension theory of dynamical systems
Secondary: 28A80: Fractals
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 2 , May 2018 , pp. 387 - 400
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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