Kvadratiske polynomier som renormaliserings grænse af degenererende quadratiske rational afbildninger

Description

It is well established that degerating quadratic rational maps (maps diverging to infinity in moduli space) have normalizations which converges to Möbius transformations. It is less known, but a fact that the same sequences may have other normalizations under which some particular iterate converges (non-uniformly) to a parabolic quadratic rational map with a fixed point of multiplier 1. In this talk I show that the very same sequences may have other normalizations of another higher iterate, converging to a quadratic polynomial. This augments the dynamical compactification of moduli space with a countable bunch of spheres.