The rigidity of reducibility of cocycles on SO(N,\mathbb{R})

Abstract

In this paper, we prove that for almost all and constant , if an analytic one-dimensional quasi-periodic cocycle (α, A) on is conjugated to the constant cocycle (α, C) by a measurable conjugacy (0, B), then it can be analytically reduced to (α, C). The proof is based on Krikorian's renormalization scheme and a local result (i.e. A is close to a constant) in Hou and You (Discrete Contin. Dyn. Syst. at press).