Hyperbolic fixpoint - Revision history

Bo198214: forgot some terms

2011-06-09T18:11:11Z

forgot some terms

2011-06-07T12:20:46Z

changed p to a

2011-06-07T12:20:17Z

added reference to Schröder coordinates

2011-06-05T11:59:27Z

draft

New page

A hyperbolic fixpoint is a [[fixpoint]] $p$ of $f$ such that $|f'(p)|\neq 0,1$.

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 A hyperbolic fixpoint is a [[fixpoint]] $a$ of $f$ such that $|f'(a)|\neq 0,1$.
-For a locally analytic function with hyperbolic fixpoint at $0$, i.e. $f(z)=c_1 z + c_2z^2$, $|c_1|\neq 0,1$, there is always a locally analytic and injective function $\sigma$ that satisfies the [[Schröder equation]]
+For a locally analytic function with hyperbolic fixpoint at $0$, i.e. $f(z)=c_1 z + c_2z^2 + \dots$, $|c_1|\neq 0,1$, there is always a locally analytic and injective function $\sigma$ that satisfies the [[Schröder equation]]
 $$\sigma(f(z))=c_1 \sigma(z))$$
 $\sigma$ is unique up to a multiplicative constant and is called the [[Schröder coordinates]] of $f$ at 0.

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-A hyperbolic fixpoint is a [[fixpoint]] $p$ of $f$ such that $|f'(p)|\neq 0,1$.
+A hyperbolic fixpoint is a [[fixpoint]] $a$ of $f$ such that $|f'(a)|\neq 0,1$.
 For a locally analytic function with hyperbolic fixpoint at $0$, i.e. $f(z)=c_1 z + c_2z^2$, $|c_1|\neq 0,1$, there is always a locally analytic and injective function $\sigma$ that satisfies the [[Schröder equation]]
 $$\sigma(f(z))=c_1 \sigma(z))$$
 $\sigma$ is unique up to a multiplicative constant and is called the [[Schröder coordinates]] of $f$ at 0.

← Older revision		Revision as of 12:20, 7 June 2011
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	A hyperbolic fixpoint is a [[fixpoint]] $p$ of $f$ such that $\|f'(p)\|\neq 0,1$.		A hyperbolic fixpoint is a [[fixpoint]] $p$ of $f$ such that $\|f'(p)\|\neq 0,1$.
		+
		+	For a locally analytic function with hyperbolic fixpoint at $0$, i.e. $f(z)=c_1 z + c_2z^2$, $\|c_1\|\neq 0,1$, there is always a locally analytic and injective function $\sigma$ that satisfies the [[Schröder equation]]
		+	$$\sigma(f(z))=c_1 \sigma(z))$$
		+	$\sigma$ is unique up to a multiplicative constant and is called the [[Schröder coordinates]] of $f$ at 0.