  The study of the dynamics of a surface homeomorphism in the neighbourhood of
an isolated fixed point leads us to the following results. If the fixed point
index is greater than 1, a family of attractive and repulsive petals is
constructed, generalizing the Leau-Fatou flower theorem in complex dynamics. If
the index is less than 1, we get a family of stable and unstable branches,
generalizing the stable manifold theorem in hyperbolic dynamics.
