On parabolic external maps

Abstract

We prove that any $C^{1+BV}$ degree $d\ge 2$ circle covering $h$ having all periodic orbits weakly expanding, is conjugate in the same smoothness class to a metrically expanding map. We use this to connect the space of parabolic external maps (coming from the theory of parabolic-like maps) to metrically expanding circle coverings.

Cited by in corpus (2)

• Fatou's associates
• Mating parabolic rational maps with Hecke groups