While the classification of univariate power series up to coordinate change
is trivial in characteristic 0, this classification is very different in
positive characteristic. In this note we give a complete classification of
univariate power series f∈K[[x]], where K is an algebraically closed
field of characteristic p>0 by explicit normal forms. We show that the right
determinacy of f is completely determined by its support. Moreover we prove
that the right modality of f is equal to the integer part of μ/p, where
μ is the Milnor number of f. As a consequence we prove in this case that
the modality is equal to the proper modality, which is the dimension of the
μ-constant stratum in an algebraic representative of the semiuniversal
deformation with trivial section.Comment: 17 pages, final versio