Michael Herman and P-J Yoccoz prove that every power series \(f(T)=\lambda T+\sum\limits_{i=2}^\infty a_iT^i \in Q_p[\![T]\!]\) such that \(\|\lambda\|=1\) and \(\lambda\) is not a root of unity is linearizable. They asked the same question for polynomials over \(F_p[\![T]\!]\), a completed discrete valuation ring of positive characteristic.

In this paper, we prove that, on opposite, most such polynomials in this case are more likely to be non-linearizable. More precisely, we give a sufficient condition of a polynomial in this form being linearizable. In particular, we prove that any polynomial of the form \(\lambda T+a_2T^2+a_pT^p\) is not linearizable.