Thurston and McMullen rigid theories reviewed: new proof and generalization

Title: Thurston and McMullen rigid theories reviewed: new proof and generalization

Speaker: Professor Ji Zhuchao (West Lake University)

Time: April 20, 2023 (Thursday) 14:10-15:00

Location: Room 312, Building 2, Hainayuan, Zijingang Campus

Abstract: This is a joint work with Junyi Xie In 1987, McMullen proved a remarkable rigidity theorem which asserts that aside from the flexible Lattès family, the multiplier spectrum of periodic points determines the conjugacy class of rational maps up to finitely many choices.  The proof relies on Thurston's rigidity theorem for post-critically finite maps, in where Teichmüller theory is an essential tool. In this talk we give a new proof of McMullen's theorem without using quasiconformal maps or Teichmüller theory.  We also show that aside from the flexible Lattès family, the length spectrum of periodic points determines the conjugacy class of rational maps up to finitely many choices. This generalize the aforementioned McMullen's theorem.

Contact person: Professor Ye Hexi (yehexi@zju.edu.cn)