Time: 09:30, Wednesday, February 28, 2024

Venue: 5th floor, A6 Building

Abstract: In this talk, I will start by recalling the basic notions of periodic cycles, eigenvalues along a periodic cycle of a rational map (i.e. a holomorphic endomorphism of CP1). Then I will introduce some basic definitions related to the dynamical system induced by a holomorphic endomorphism of CP^n with n ≥ 2, and the notion of post-critically finite for such endomorphisms. I will present several ways to construct post-critically finite endomorphisms and I will focus on Koch's construction. The main objective is to prove the conjecture for the case of Koch maps. The proof is based on the technique applied in a broader family of endomorphisms: post-critically finite all the way down endomorphisms.