p-进动力系统的研究涉及到复分析、动力系统、遍历论、数论、交换代数、非阿基米德域和Berkovich空间等多个方向，是当前国际上广受关注的新兴和热点领域。 p-进动力系统研究p-进数域上函数迭代形成的动力系统，主要包括“复”p-进动力系统（主要研究p-进复数域及Berkovich空间上函数的Fatou集和Julia集性质）和“实”p-进动力系统（主要研究p-进数域上动力系统极小性和极小分解）。. 本项目计划研究p-进 “实”数域上有理函数的动力系统混沌性质，主要内容包括：寻找混沌存在的条件；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；研究特殊有理函数（双曲、临界有限等）的动力力学行为，通过拓扑有限子位移或者拓扑Markov链来刻画其混沌性。

p-adic dynamical systems is a new research field which having drawn considerable attention in the mathematical community. This research topic is closely related to complex analysis, dynamical systems, ergodic theory, number theory, commutative algebra, non-Archimedean field and Berkovich space etc. The central theme of p-adic dynamical system is studying the iterations of p-adic function on p-adic field which mainly contains “complex” (investigating Fatou and Julia sets of functions on the field C_p of “complex” p-adic numbers or Berkovich space ) and “real” p-adic dynamical systems (investigating the minimality and minimal decomposition of functions on the field Q_p of p-adic numbers)... This project will investigate the chaotic behavior of rational maps on the field Q_p of p-adic numbers. The goals of this research are: to obtain the condition under which does chaos exist; to investigate the relation of the dynamical system of rational map on the fields Q_p and those on the field extensions of Q_p; to investigate the dynamical behavior of special rational maps (hyperbolic, post critical finite etc) by conjugating the chaotic parts to subshifts of finite type or topological Markov chains.