Combinatorial Non-Rigidity for Infinitely Renormalizable Unicritical Cubic Polynomials
发布时间：2026年04月15日
浏览次数：3
发布者: Xiaoni Tan
主讲人： Hiroyuki Inou (Kyoto University, Japan)
活动时间： 从 2026-04-16 09:00 到 10:00
场地： Online
Abstract:
McMullen had conjectured that every polynomial with connected Julia set without indifferent cycle is combinatorially rigid. This conjecture for degree two implies the local connectivity of the Mandelbrot set. On the other hand, Henriksen gave a counterexample of this conjecture, which is cubic polynomials having infinitely many quadratic renormalizations that capture the critical point outside.
We prove that there exists a cubic infinitely renormalizable unicritical polynomial which is not combinatorially rigid. More precisely, we construct a cubic polynomial with two distinct critical points having infinitely many cubic renormalizations. Hence, its combinatorial class contains a unicritical polynomial.
This is a joint work with Yimin Wang.
Zoom Meeting ID: 181 155 584
