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).