报告人：Zhiqiang Li（Stony Brook）
时间：2018-12-14 14:00-15:00
地点：Room 1560, Sciences Building No. 1
复动力系统中的最小周期轨定理
举杯邀明月，对影成三人。Ruelle zeta函数是动力系统对黎曼的一份邀约，却因此串联起数论、动力系统和几何三大领
域。黎曼zeta函数的重要性质借由动力系统显现，不仅能加深人们对动力性质的认识，更能解释动力系统和几何信息的
深刻关联。最小周期轨定理（Prime Orbit Theorem）便是其中一例：它神似素数定理（Prime Number Theorem），形同
素测地线定理（Prime Geodesic Theorem），影伴拉普拉斯和Ruelle算子，半个世纪以来热度不减。最小周期轨定理和素
测地线定理缘何俘获众心？Ruelle zeta函数又何以幻化万千？12月14日下午2点李智强博士将为您浅释其中缘由，并讲述
复动力系统中最小周期轨定理的最新研究进展。
Periodic orbits and geodesics play important roles in the study of dynamics and geometry, respectively. In
resemblance to the classical Prime Number Theorem in number theory and its relation to the Riemann
Hypothesis, it is a natural problem to investigate precise asymptotes for the number of (primitive) periodic
orbits and (closed) geodesics, as well as the corresponding error terms. Such results, often known as Prime
Orbit Theorems and Prime Geodesic Theorems, have been established in many dynamical and geometric contexts.
In this talk, we are going to give a brief overview on the history of such results in dynamics and geometry as
well as their connections. We will focus on the recent discoveries of Prime Orbit Theorems in complex
dynamics, a vibrant branch of dynamical systems, concentrating on the study of iterated rational maps
(i.e., quotients of polynomials) on the Riemann sphere.
相关附件
Abstract.pdf
