Pseudo-monodromy and the Mandelbrot set

We investigate the discontinuity of codings for the Julia set of a quadratic map. To each parameter ray, we associate a natural coding for Julia sets on the ray. Given a hyperbolic component H of the Mandelbrot set, we consider the codings along the two parameter rays landing on the root point of H. Our main result describes the discontinuity of these two coding 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.