Abstract:

In this talk I will present a joint work with Núria Fagella giving an approximation result for the bifurcation locus of an analytic family depending analytically with respect to one parameter. In particular, we will define a set C such that C' contains the boundary of the bifurcation locus (adequately defined). This approximation is a generalisation of the classical result of the accumulation of centres of hyperbolic components in the boundary of the Mandelbrot set. I will also give some ideas about specific cases when the inclusion is an equality.