p-进动力系统的研究涉及到复分析、动力系统、遍历论、数论、非阿基米德分析和Berkovich空间理论等多个方向，是当前国际上广受关注的热点领域。p-进动力系统研究p-进数域上函数迭代形成的动力系统。本项目计划研究p-进“实”数域上有理函数的动力系统的整体结构，主要内容包括：得到具有潜在好约化有理函数动力系统的极小性判定准则；探讨有正熵的极小有理函数的存在性；建立p-进“实”数域上有理函数动力系统与扩域上动力系统之间的联系；利用p-进“复”数域及Berkovich空间上有理函数动力系统的现有理论来研究p-进“实”数域上有理函数的动力学行为，并引入可数符号动力系统来刻画一般有理函数的混沌性。

The research of p-adic dynamical systems, which attracts much attention in the mathematical community, is closely related to complex analysis, dynamical systems, ergodic theory, number theory, non-Archimedean analysis and Berkovich space etc. This project will study the global structures of dynamical systems generated by rational maps on the projective line over the field Q_p of p-adic numbers. The goals of this research are: to obtain the criterion for the minimality of rational maps which have potential good reduction; to investigate the existence of the minimal rational maps which has positive entropy; to establish the relation between the dynamical systems of rational maps on the fields Q_p and those on the field of extensions of Q_p; to investigate the global dynamical behavior of rational maps by using the countable symbolic dynamical systems and the known results concerning the dynamical systems over complex p-adic fields and Berkvich spaces.