报告人：李兵 教授（华南理工大学）

时间：2026年01月10日 14:30-

地址：理科楼LA104

摘要：In the talk, we show that if $S\subseteq\R^d$ is hyperplane absolute winning on a closed hyperplane diffuse set $L\subseteq\mathbb{R}^d$, then $\dim_{\rm H} S\cap K=\dim_{\rm H} K$ for any irreducible self-conformal set $K\subseteq L$ without assuming any separation condition on $K$.  The result is then applied to obtain the Hausdorff dimension of intersections between irreducible self-conformal sets and twisted non-recurrent sets $\mathrm{N} (T, \mathcal{G})$ defined as

   \begin{equation*} \mathrm{N}(T,\mathcal{G}):=\left\{\mathbf{x}\in[0,1]^d:\liminf_{n\to\infty}\|T^n(\mathbf{x})-g_n(\mathbf{x})\|>0\right\},

   \end{equation*}

     where $T:[0,1]^d\to[0,1]^d$ belongs to a broad class of product maps, $\mathcal{G}:=\{g_n\}_{n\in\mathbb{N}}$ is a sequence of self-maps on $[0,1]^d$ with uniform Lipschitz constant and $\|\cdot\|$ denotes the maximal norm in $\mathbb{R}^d$. When $T$ is the $\beta$-transformation on $[0,1]$, it provides a positive answer to a question raised informally by Broderick, Bugeaud, Fishman, Kleinbock and Weiss (Math. Res. Lett., 2010). For the case $T$ is a $d\times d$ diagonal matrix transformations, our results provide a partial answer asked in a paper of Li, Liao, Velani and Zorin (Adv. Math., 2023). A natural generalization to non-autonomous setting is also obtained. This is a joint work with Junjie Huang, Bo Wang and Na Yuan.

邀请人：孔德荣

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