发表机构
School of Mathematics and Statistics, Wuhan University; School of Mathematics, Guangdong University of Education（武汉大学数学与统计学院; 广东教育学院数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对单位区间上含 sofic β-变换等的扩张马尔可夫映射，研究动态 badly approximable 点的定量回归性质，确定回归集与 badly approximable 集等交集的豪斯多夫维数，得到相关结果。
AI 中文摘要
我们研究单位区间上的一类扩张马尔可夫映射，包括 sofic β-变换、高斯映射、帐篷映射和 cookie-cutter 映射。我们探究动态 badly approximable 点的定量回归性质，这类点的轨道最终与给定点保持正距离。我们证明，回归集与 badly approximable 集交集的豪斯多夫维数由与对应回归集相同的压力函数决定。我们进一步得到两类相关交集的豪斯多夫维数：回归集与非回归集的交集，以及收缩目标集与 badly approximable 集的交集。
英文摘要
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.
