LINEAR MAPS GIVEN BY QUADRATIC POLYNOMIALS
Quadratic maps of a speciﬁc type, deﬁned on ﬁnite ﬁelds of characteristic two, are studied in terms of conjugacy maps, tree structures, and periodic points. In terms of conjugacy, it is found that conjugate ﬁeld elements yield conjugate maps. Convenient bases for the sets of nilpotent and periodic points are determined separately. From these bases, various previous results are obtained with little reliance on matrix-based methods, allowing more eﬃcient methods to be implemented as they arise.