  In this paper we introduce the notion of parabolic-like mapping, which is an
object similar to a polynomial-like mapping, but with a parabolic external
class, i.e. an external map with a parabolic fixed point. We prove a
straightening theorem for parabolic-like maps, which states that any
parabolic-like map of degree 2 is hybrid conjugate to a member of the family
Per_1(1), and this member is unique (up to holomorphic conjugacy) if the filled
Julia set of the parabolic-like map is connected.
