p-进位系统的一类集值映射

摘要

考虑 p-进位系统及其诱导的超空间映射的一些动力学性质，根据底空间系统与超空间系统的关系证明了 p-进位系统诱导的一类集值映射是连续的且等距的，并证明了这类集值映射的拓扑熵为0并且不是 Li-Yorke 混沌的。%Some dynamical properties of p-adic system and the set-valued maps induced by p-adic maps were considered.With the help of the relation of the base system and its hyperspace system,a class of set-valued maps of p-adic system was proved to be continuous and isometric.Furthermore,it was proved that the set-valued maps have 0 topological entropy and are not Li-Yorke chaotic.