动力系统研讨班报告
报告人：Prof. Lingmin Liao (LAMA Université Paris-Est Créteil, France)
题 目：Distance between two orbits of a dynamical system
时 间：2018.07.31（星期二）, 09:30-10:30
地 点：数学院南楼N602室
摘 要：Let $(X, T, \mu)$ be a measure-preserving dynamical system, where the space $X$ is equipped with a metric $d$. For two points $ x, y \in X$, and a positive integer $n$, define $m_n (x, y)$ as the smallest distance between the orbit points $T^i x$ and $T^j y$ with $0 \leq i , j \leq n-1$. The asymptotic behavior of $m_n(x, y)$ is studied. It is proved that under certain rapid mixing conditions of the dynamical system, $\mu \times \mu$-almost surely $ -\log m_n (x, y) / \log n $ converges to the constant $2 / C_{\mu}$, where $C_{\mu}$ is the correlation dimension of the measure $\mu$. For irrational rotations, the behavior is different. The irrationality exponent of the angle of rotation is involved. This is a joint work with Vanessa Barros and Jér？me Rousseau.
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报告人：Prof. Shilei Fan (Central China Normal University)
题 目：Tiling and spectral sets in finite groups
时 间：2018.07.31（星期二）, 10:40-11:40
地 点：数学院南楼N602室
摘 要：Fuglede conjectured that a Borel set of positive finite Lebesgue measure is a spectral set (admitting orthogonal exponential bases) if and only if it tiles the space by translation. It is dispoved by Tao et al. for high dimensional(>2) space. However, the conjecture remains open in real line and plane. Fuglede's conjecture can be naturally stated for other groups, for example Z. These cases are not only interesting on their own, but they also have connection with the original case. I will introduce the recent progress on the finite setting.
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