Difference between revisions of "Super-attracting fixpoint"
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| − | A fixpoint $ | + | A fixpoint $a$ of $f$ such that $f'(a)=0$. |
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| + | For an at $0$ analytic function $f(z)=c_p z^p + c_{p+1}z^{p+1} + \dots$, $p\ge 2$, $c_p\neq 0$, one can always find a locally analytic and injective function $\beta$ such that the [[Böttcher equation]] $\beta(f(z))=\beta(x)^p$ is satisfied. $\beta$ is called the [[Böttcher coordinate]]. | ||
Revision as of 12:11, 7 June 2011
A fixpoint $a$ of $f$ such that $f'(a)=0$.
For an at $0$ analytic function $f(z)=c_p z^p + c_{p+1}z^{p+1} + \dots$, $p\ge 2$, $c_p\neq 0$, one can always find a locally analytic and injective function $\beta$ such that the Böttcher equation $\beta(f(z))=\beta(x)^p$ is satisfied. $\beta$ is called the Böttcher coordinate.