Location: Zoom (ID: 690 5359 1120, Password: 294214)

Abstract: In complex dynamics, an interesting question is to determine which kinds of hyperbolic components are bounded in the moduli space of rational maps. In this talk, we study this problem in a well-known slice called Newton family. We prove that, in the moduli space of quartic Newton maps, a hyperbolic component is bounded if and only if it is not type-IE(immediately escaping); furthermore, the GIT-compactification of each type-IE hyperbolic component at infinity boundary is either an analytic closed disk or one point. The proof is based on a convergence theorem of internal rays we establish for degenerate Newton sequences. This is a joint work with Hongming Nie.