关于举行韩国仁荷大学Jeong Sangtae 教授学术报告会的通知

报告题目：Ergodic decomposition for a class of B-functions on the ring of p-adic integers

报  告  人：Jeong Sangtae   教授(韩国仁荷大学（Inha University）)

报告时间：2019年8 月10 日（星期六）上午 9:00-10:00                

报告地点：4号楼318室

邀  请  人：胡甦  副教授

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数学学院

2019年8 月7 日

报告摘要：

In this talk, we present the ergodicity criteria for certain $1$-Lipschitz functions on $\Z_p$, which are known as $\mathcal{B}$-functions, in terms of the Mahler and van der Put expansions. These functions are locally analytic functions of order $1$ (and therefore contain polynomials). For arbitrary primes $p\geq 5,$  an ergodicity  criterion  of $\mathcal{B}$-functions on $\Zp$ is introduced, which leads to an efficient and practical method of constructing ergodic polynomials on $\Z_p$ that realize a given unicyclic permutation modulo $p.$ Thus, a complete description of ergodic polynomials modulo $p^{\mu},$ which are reduced from all ergodic $\mathcal{B}$-functions on $\Zp,$ is provided where $\mu=\mu(p)$ = 3 for $p\in \{2,3\}$ and $\mu =2$ for $p\geq5.$