Dynamics Seminar

Event Information Pseudo-monodromy and the Mandelbrot set
14:10 on Wednesday March 20, 2024
15:00 on Wednesday March 20, 2024
Stewart Library, Fields Institute, 222 College St.
Yutaka Ishii
Kyushu University

We investigate the discontinuity of two codings for the Julia set of a quadratic map as one approaches the root point $r_H$ of a hyperbolic component $H$ of the Mandelbrot set along the two parameter rays landing at $r_H$. Our main result describes this discontinuity in terms of the kneading sequences of the hyperbolic components which are conspicuous to $H$. This result can be interpreted as a solution to the degenerated case of Lipa's conjecture on the monodromy problem of the horseshoe locus for the complex H\'enon family. This is joint work with Thomas Richards (Kyushu University).

This talk will take place in Fields Institute, Room 309 (the library).