发表机构
Fudan University; University of Toronto; Peking University; Great Bay University and Great bay institute for advanced study（复旦大学; 多伦多大学; 北京大学; 大湾区大学和大湾区高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了$C^r$通用表面排斥子的维数公式，推广了满足强分离条件的平面非线性迭代函数系统吸引子的维数结果，并弱化了Weierstrass型函数图像二分结果的正则性要求。
AI 中文摘要
我们证明，对于一个$C^r$通用表面排斥子（$1 < r \leq \infty$），其Hausdorff维数与盒维数恰好是次可加拓扑压力函数的唯一零点。作为该框架的应用，我们表明满足强分离条件（SSC）的一致非共形且弱不可约的平面非线性迭代函数系统（IFS）的吸引子达到其预期的Hausdorff维数与盒维数。此外，作为通用排斥子定理的直接推论，我们推导出该维数公式对满足SSC的通用$C^r$平面IFS也成立。利用该方法，我们还推广了Ren和Shen（2021）关于Weierstrass型函数图像的二分结果，将其实解析要求弱化至$r > 1$时的任意$C^r$正则性。
英文摘要
We establish that for a $C^r$-generic surface repeller ($1 < r \leq \infty$), 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 (2021) by weakening their real-analytic requirement to arbitrary $C^r$ regularity for $r > 1$.
Comments92 pages
