  Given a polynomial or a rational map f we associate to it a space of maps. We
introduce local coordinates in this space, which are essentially the set of
critical values of the map. Then we consider an arbitrary periodic orbit of f
with multiplier \rho\not=1 as a function of the local coordinates, and
establish a simple connection between the dynamical plane of f and the function
\rho in the space associated to f. The proof is based on the theory of
quasiconformal deformations of rational maps. As a corollary, we show that
multipliers of non-repelling periodic orbits are also local coordinates in the
space.
