Speaker: Prof.Jeong Sangtae（Inha University）

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

Time: Sat, Aug.10 2019, AM: 9:00-10:00

Location: Room 4318, Building No.4, Wushan Campus

Abstract:   

      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 $p\geq5.$