Difference between revisions of "Fixpoint"
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A fixpoint $p$ of a function $f$ is a value such that $f(p)=p$. | A fixpoint $p$ of a function $f$ is a value such that $f(p)=p$. | ||
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| + | If $f$ is a holomorphic function, we define the multiplicity of the fixpoint $p$ to be the [http://en.wikipedia.org/wiki/Zero_(complex_analysis) multiplicity of the zero] of $f(z)-z$ at $p$. | ||
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| + | For example $z+z^2$ has multiplicity 2 at fixpoint 0, $2z+z^2$ has multiplicity 1 at fixpoint 0. | ||
Latest revision as of 11:57, 1 May 2013
A fixpoint $p$ of a function $f$ is a value such that $f(p)=p$.
If $f$ is a holomorphic function, we define the multiplicity of the fixpoint $p$ to be the multiplicity of the zero of $f(z)-z$ at $p$.
For example $z+z^2$ has multiplicity 2 at fixpoint 0, $2z+z^2$ has multiplicity 1 at fixpoint 0.