报告人：Michal Rams 教授 (波兰科学院)

时间：2026年01月08日 09:30-

地址：理科楼LA104

摘要：The question of describing the Hausdorff dimension of the set of points which continuous fraction expansion has a subsequence growing with prescribed exponential speed was solved by Wang and Wu in 2008. In 2018 Kleinbock and Wadleigh solved a question of exponentially growing products of two consecutive digits, this question was then generalized in several direction (more than two digits, weighted products, ...).

In the presented result, joint with A. Bakhtawar, we describe the Hausdorff dimension of the set

\[

\{x; \prod_{j=1}^k a_{n+i_j}^{t_j}(x) \geq B^n {\rm i.o.}\},

\]

where $t_1,\ldots, t_k >0$, $B>1$, and $i_1<\ldots<i_k$. We do our construction not just for the Gauss map, but for more general $d$-decaying Gauss-like systems (a class containing in particular the Gauss map and its most popular modifications). We do not assume any distortion property, which means we need first to prove some basic thermodynamical properties of $d$-decaying Gauss-like systems (in particular, we need to prove the existence of geometric pressure).

邀请人：数学研究中心

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