Intersections of quantitative recurrence and badly approximable sets for expanding Markov maps
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Liao, Lingmin, Yuan, Na
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221183746