Let f be a (germ of ) holomorphic self-map of ℂ2 such that the origin is an isolated fixed point and such that dfO=id. Let v(f) be the degree of the first nonvanishing term in the homogeneous expansion of f−id. We generalize to ℂ2 the classical Leau-Fatou flower theorem proving that there exist v(f)−1 holomorphic curves f-invariant, with the origin in their boundary, and attracted by O under the action of f.
"The residual index and the dynamics of holomorphic maps tangent to the identity." Duke Math. J. 107 (1) 173 - 207, 1 March 2001. https://doi.org/10.1215/S0012-7094-01-10719-9