Quantitative recurrence problem on some Bedford-McMullen carpets
Yu-Liang Wu, Na Yuan
TL;DR
This paper investigates the Hausdorff dimension of the quantitative recurrent set for a specific endomorphism on Bedford-McMullen carpets where the Hausdorff and box dimensions coincide.
Contribution
It provides new results on the Hausdorff dimension of recurrent sets in Bedford-McMullen carpets with equal Hausdorff and box dimensions.
Findings
Determined the Hausdorff dimension of the recurrent set.
Established conditions under which the Hausdorff and box dimensions are equal.
Extended understanding of recurrence properties in self-affine fractals.
Abstract
In this paper, we study the Hausdorff dimension of the quantitative recurrent set of the canonical endomorphism on the Bedford-McMullen carpets whose Hausdorff dimension and box dimension are equal.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Advanced Topology and Set Theory