Martingales for Quasisymmetric Systems

CCNY Dynamical Systems Seminar

Time and place

1 PM on Tuesday, December 7th, 2010; NAC 6-113

Yunchun Hu (Graduate Center, CUNY)

Abstract

I will introduce the dual symbolic space for uniformly quasisymmetric circle endomorphisms of degree d>1. For this purpose, I’ll construct a sequence of Markov partitions for each uniformly quasisymmetric circle endomorphism and this sequence of Markov partitions has bounded and bounded nearby geometry. For those endomorphisms which preserve the Lebesgue measure, we further construct a uniformly bounded martingale sequence, and then use the martingale convergence theorem to show this sequence has a L_1 limit. This is joint work with Yunping Jiang and Zhe Wang.