中科院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

学术报告

多复变与复几何研讨班

SCV&CG Seminar

报告人：仲国磊 (IBS Center for Complex Geometry)

题  目：Periodic points for meromorphic self-maps of Fujiki varieties

时  间：2024.01.11（星期四）15:30-17:30

地  点：南楼N913

摘  要：As one of the fundamental problems in complex dynamics, the equidistribution of periodic points is expected to impose rather strong ergodic properties on the dynamical system. It was proved by Dinh-Nguyễn-Truong that, given a meromorphic self-map of a compact Kähler manifold which has a dominant topological degree, the set of isolated periodic points is asymptotically equidistributed with respect to the equilibrium measure. In this talk, we consider a dominant meromorphic self-map of a (possibly singular) complex Fujiki variety. If the topological degree is strictly larger than the other dynamical degrees, based on the work of Dinh-Nguyễn-Truong, we show that the number of isolated periodic points grows exponentially fast similarly to the topological degrees of the iterates; this allows us to give an affirmative answer to a conjecture of Shou-Wu Zhang. In the general case, we show that the exponential growth of the number of isolated periodic points is at most the algebraic entropy. This is based on a joint work with Tien-Cuong Dinh.