Non-linearizability of polynomials at irrationally indifferent fixed points

Abstract

In this paper, we consider the non-linearizability of polynomials with irrationally indifferent fixed points. Under the assumption that there exists a cubic polynomial which is linearizable at an irrationally indifferent fixed point with a non-Brjuno multiplier, we show that, for every degree more than two, one can construct a holomorphic family of possible maximal dimension consisting of polynomials linearizable at the fixed point.