Fatou coordinate

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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): $$f(z)=z+c_{m+1}z^{m+1} + c_{m+2}z^{m+2} + \dots $$


  • Milnor, J. (2006). Dynamics in one complex variable. 3rd ed. Princeton Annals in Mathematics 160. Princeton, NJ: Princeton University Press. viii, 304 p.