Difference between revisions of "Perturbed Fatou coordinates"

Latest revision as of 14:42, 5 June 2011

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-While [[Fatou coordinates]] are the (injective parts of the) [[principal Abel function]]s of a holomorphic function $f$ at a given fixpoint,
+#REDIRECT [[perturbed Fatou coordinate]]
-for simplicity this fixpoint is assumed to be at 0:
-$$f(z)= z + c_{m+1} z^{m+1} + o(z^{m+1}),$$
-'perturbed' Fatou coordinates refer to a function that is 'disturbed' by some small $c_0\in\C$:
-$$f(z)=c_0 + z + c_{m+1} z^{m+1} + o(z^{m+1})$$
-This function usually has $2m$ fixpoints in a vicinity of 0.
-For the details of the case $m=1$ I refer to [[Shishikura_perturbed_Fatou_coordinates|Shishikuras presentation]].