Speaker: Hiroyuki Inou, Kyoto university
January 10, 2024 10:15 AM
- 11:15 AM
Abstract:
The well-known conjecture that the Mandelbrot set is locally connected is closely related to the combinatorial rigidity for infinitely renormalizable combinatorics. Henriksen proved that the combinatorial rigidity conjecture does not hold for the cubic family. His counterexamples are cubic polynomials having infinitely many renormalizations of capture type. Hence their critical points are combinatorially separated.
We present another counterexample of the combinatorial rigidity conjecture having infinitely many cubic renormalizations. Such an example has two distinct critical points which are combinatorially equivalent and is contained in the combinatorial class of an infinitely renormalizable unicritical polynomial. We would also discuss its dynamical behavior.