Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	仲国磊, IBS Center for Complex Geometry
Inviter:	周向宇院士
Title:	Periodic points for meromorphic self-maps of Fujiki varieties
Language:	Chinese
Time & Venue:	2023.01.11 15:30-17:30 南楼N913
Abstract:	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-Nguy?n-Truong that, given a meromorphic self-map of a compact K?hler 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-Nguy?n-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.