Degenerate characteristic directions for maps tangent to the Identity
  Let F be a germ of (C^2,O) tangent to the identity. Assume F has a characteristic direction [v]. In [Hak] Hakim gives conditions to guarantee the existence of an attracting basin to the origin along [v], in the case of [v] a non-degenerate characteristic direction. In this paper we give conditions to guarantee the existence of basins along [v] in the case of [v] a degenerate characteristic direction. 
Liz Vivas
math.CV math.DS