Recurrence to shrinking targets on typical self-affine fractals
Henna Koivusalo, Felipe A. Ram\'irez
TL;DR
This paper investigates the Hausdorff dimension of points on self-affine fractals that recurrently approach shrinking targets, using symbolic recurrence sets to analyze their properties.
Contribution
It introduces a method to determine the Hausdorff dimension of recurrence sets on self-affine fractals via symbolic dynamics.
Findings
Dimension formulas for recurrence sets on self-affine fractals
Equivalence between symbolic recurrence sets and fractal recurrence sets in many cases
New insights into the structure of recurrence on self-affine fractals
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.
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