理学院学术报告-Genetics of iterative roots for PM functions

报告题目：Genetics of iterative roots for PM functions

报告人：刘鎏

报告时间：2023年9月11日9：00—9：50

报告地点：二教2B-409

报告人简介：刘鎏，西南交通大学数学学院副教授，2012年毕业于四川大学，2012-2014年在中国科学院数学与系统科学研究所做博士后。目前，从事映射的迭代与嵌入的动力学及相关的函数方程研究，包括与迭代根、嵌入流及不变流形相关的迭代方程，与线性化及正规形相关的共轭方程。已在国际和国内重要学术期刊《Discrete Contin. Dyn. Syst.》、《J. Math. Anal. Appl.》、《Nonlinear Analysis》、《J. Diff. Equ. Appl.》、《Aequationes Math.》、《中国科学》等发表论文十多余篇。主持一项国家自然科学基金青年基金项目，一项四川省科技厅青年基金项目。曾获2017年第55届ISFE国际会议ISFE Medal。 

报告摘要：It is known that the time-one mapping of a flow defines a discrete dynamical system with the same dynamical behaviors as the flow, but conversely one wants to know whether a flow embedded by a homeomorphism preserves the dynamical behaviors of the homeomorphism. In this paper we consider iterative roots, a weak version of embedded flows, for the preservation. We refer an iterative root to be genetic if it is topologically conjugate to its parent function. We prove that none of PM functions with height being >1 has a genetic root and none of iterative roots of height being >1 is genetic even if the height of its parent function is equal to 1. This shows that most functions do not have a genetic iterative root. Further, we obtain a necessary and sufficient conditions under which a PM function $f$ has a genetic iterative root in the case that $f$ and the iterative root are both of height 1.