多复变与复几何研讨班:Recursive inequalities and dynamical degrees

中科院数学与系统科学研究院

数学研究所

学术报告

多复变与复几何研讨班

报告人：谢俊逸 教授（北京大学）

题  目：Recursive inequalities and dynamical degrees

时  间：2024.01.17（星期三）下午3:30-5:00

地  点：晨兴110

摘  要：For every dominant rational self-map, we find a family of recursive inequalities of some dynamically meaningful cycles.  Applying these recursive inequalities, we proved serval results in algebraic dynamics. We get an algorithm to compute the dynamical degrees to arbitrary precision. We proved that for a family of dominant rational self-maps, the dynamical degrees are lower semi-continuous with respect to the Zariski topology, this proves a conjecture of Call and Silverman. We proved that the set of periodic points of a cohomologically hyperbolic rational self-map is Zariski dense.