The dynamics of holomorphic germs tangent to the identity near a smooth curve of fixed points

摘要

Let f is an element of End(C-2, O) be tangent to the identity and with order v(f) >= 2. We Study the dynamics of f near the set of his fixed points. Using some known results in this domain, we prove that if the set of fixed points of f is smooth at the origin, f is tangential to this set, and the origin is not singular, then there are no parabolic Curves for f at the origin. After that, We use some adapted techniques to prove the existence of (v(f) - 1) parabolic Curves for f at the origin if the set of fixed points of f is smooth at the origin and this last one is a singular point of f with the pure order of f v(0)(f) = 1. Finally, we prove that if the origin is dicritical. then there exist infinitely many parabolic Curves. (c) 2008 Elsevier Masson SAS. All rights reserved.