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arXiv · 2606.06012

Weighted topological entropy and intersecting random translates of Bedford--McMullen carpets

Nima Alibabaei·Masaki Tsukamoto
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Abstract

We establish a relativised variational principle for the Feng--Huang weighted topological entropy associated with a factor map between dynamical systems. Combined with a recent theorem of Yin, this yields an almost-everywhere equivalence between the Feng--Huang entropy and its combinatorial version on fibers. As an application, we compute the Hausdorff dimension of the intersection of random translates of two Bedford--McMullen carpets. The resulting formula extends the Kenyon--Peres formula from the self-similar to the self-affine setting, and also points to a new problem concerning random matrix products.

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Nima Alibabaei, Masaki Tsukamoto. 2026-06-04. Weighted topological entropy and intersecting random translates of Bedford--McMullen carpets. https://arxiv.org/abs/2606.06012

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