Fixpoint

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.