  For the study of the 2-dimensional space of cubic polynomials, J. Milnor
considers the complex 1-dimensional slice S_n of the cubic polynomials which
have a super-attracting orbit of period n. He gives in [M4] a detailed
conjectural picture of S_n. In this article, we prove these conjectures for S_1
and generalize these results in higher degrees. In particular, this gives a
description of the closures of the hyperbolic components and of the Mandelbrot
copies sitting in the connectedness locus. We prove that the closure of
hyperbolic components is a Jordan curve, the points of which are characterized
according to their dynamical behaviour. The global picture of the connectedness
locus is a closed disk together with ``limbs'' sprouting off at the cusps of
Mandelbrot copies and whose diameter tends to 0 (which corresponds to the
Yoccoz inequality in the quadratic case).
  [[M4] J. Milnor - On cubic polynomials with periodic critical point, preprint
(1991).]
