Séminaire de Systèmes Dynamiques

Multipliers of a sequence of rational maps

by Chen Gong (Polytechnique)

Europe/Paris
Description

We analyze the multipliers of a degenerating sequence in the moduli space of complex rational mpas. We show that either most periodic points have uniformly bounded multipliers, or most of them have exploding multipliers at a rate controlled by the inverse of Rumely's minimal resultant function. Furthermore we prove that there are at most 2d-2 non-trivial multiplier scales.