The residual index and the dynamics of holomorphic maps tangent to the identity

摘要

Let f be a (germ of) holomorphic self-map of C-2 such that the origin is an isolated fixed point and such that df(O) = id. Let nu (f) be the degree of the first nonvanishing term in the homogeneous expansion of f - id. We generalize to C-2 the classical Leau-Fatou flower theorem proving that there exist nu (f) - 1 holomorphic curves f-invariant, with the origin in their boundary, and attracted by O under the action of f.