  In 2011, Hefez and Hernandes completed Zariski's analytic classification of
plane branches belonging to a certain equisingularity class by creating "very
short" parameterizations over the complex numbers. Their results were used by
Mehmood and Pfister to classify unimodal plane branches in characteristic 0 by
constructing lists of normal forms. The goal of this paper is to give a
complete classification of unimodal plane branches over an algebraically closed
field of positive characteristic. Since the methods of Hefez and Hernandes are
not applicable in positive characteristic, we use a different approach and, for
some sporadic singularities in small characteristic, computations with
SINGULAR. Our methods are characteristic-independent and provide a different
proof for the classification in characteristic 0, showing at the same time that
this classification holds also in large characteristic. The main theoretical
ingredients are the semicontinuity of the semigroup and the modality, which we
prove.
