# Fatou coordinate

Fatou coordinate - a term predominantly used in holomorphic dynamics - usually refers to one of the $2m$ principal Abel functions of a holomorphic function $f$ with parabolic fixpoint (which we assume for simplicity to be located at 0): $$f(z)=z+c_{m+1}z^{m+1} + c_{m+2}z^{m+2} + \dots$$