LINEAR MAPS GIVEN BY QUADRATIC POLYNOMIALS

Abstract

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 mplemented as they arise.