Intersections of quantitative recurrence and badly approximable sets for expanding Markov maps

Lingmin Liao; Na Yuan

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arXiv · 2610.12258

Intersections of quantitative recurrence and badly approximable sets for expanding Markov maps

Lingmin Liao·Na Yuan

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Abstract

We study a class of expanding Markov maps on the unit interval, which includes sofic $β$-transformations, Gauss maps, tent maps and cookie-cutter maps. We investigate the quantitative recurrence property for points that are dynamically badly approximable, namely, points whose orbits eventually remain a positive distance from a given point. We show that the Hausdorff dimension of the intersection of a recurrence set and a badly approximable set is determined by the same pressure function as that of the corresponding recurrence set. We further obtain the Hausdorff dimensions of two related intersections: recurrence sets with non-recurrent sets, and shrinking target sets with badly approximable sets.

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BibTeX RIS

Lingmin Liao, Na Yuan. 2026-10-08. Intersections of quantitative recurrence and badly approximable sets for expanding Markov maps. https://arxiv.org/abs/2610.12258

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