学术报告：排斥子的维数理论

报告时间：2026年9月16日（星期三）上午10:00-11:00

报告地点：学院南路校区，主教216

主持人：梁超教授

报告人：许地生，大湾区大学，教授

报告摘要：We establish that for a C^r-generic surface repeller (1＜r≤\infty), its Hausdorff and box

dimensions are exactly the unique zero of the sub-additive topological pressure function. As

an application of our framework, we show that the attractor of a uniformly non-conformal

and weakly irreducible planar non-linear iterated function system (IFS) satisfying the strong

separation condition (SSC) attains its expected Hausdorff and box dimensions. Furthermore,

as a direct consequence of our generic repeller theorem, we deduce that this dimension

formula also holds for a generic C^r planar IFS satisfying the SSC. Using this approach, we

also extend the dichotomy result for graphs of Weierstrass-type functions of Ren and Shen

by weakening their real-analytic requirement to arbitrary C^r regularity for r>1.

报告人简介：许地生，大湾区大学教授，研究方向：动力系统，分形几何，谱理论，数学教育，AI4Math,曾在四大期刊中的Acta Math., Invent. Math.以及Duke Math J. , JEMS,Ann. Sci. ÉNS国际期刊发表论文，动力系统系列会议Beyond Uniform Hyperbolicity组委会成员，多次担任高中联赛、冬令营、集训队、IMO等命题阅卷工作。

撰稿人：刘洁

审稿人：邓露