Tame quasiconformal motions and monodromy

Abstract

The concept of tame quasiconformal motions was first introduced by Jiang et al. (2018). The concept of monodromy of holomorphic motions was first introduced by Beck et al. (2012). In this paper, we will show that the concept of monodromy of tame quasiconformal motions can be defined, whereas it cannot be defined for quasiconformal motions, in the sense of Sullivan and Thurston (1986). We also study some other properties of tame quasiconfor-mal motions.