Invariants and conjugacy classes of triangular polynomial maps

In this article, we classify invariants and conjugacy classes of triangular polynomial maps. We make these classifications in dimension 2 over domains containing QQ, dimension 2 over fields of characteristic p, and dimension 3 over fields of characteristic zero. We discuss the generic characteristic 0 case. We determine the invariants and conjugacy classes of strictly triangular maps of maximal order in all dimensions over fields of characteristic p  . These strictly triangular maps of maximal order turn out to be equivalent to a map of the form (x1+f1,…,xn+fn)(x1+f1,…,xn+fn) where fi∈xnp−1k[xi+1p,…,xnp] if 1≤i≤n−11≤i≤n−1 and fn∈k⁎fn∈k⁎.