= Commuting functions
{title2=$R\circ S=S\circ R$}
= Commuting maps
{synonym}
Two self-maps $R,S:X\to X$ commute when $R\circ S=S\circ R$. Induction then gives $R^n\circ S=S\circ R^n$ and $R^n\circ S^m=S^m\circ R^n$ for all nonnegative integers $m,n$. Sharing a fixed point or invariant set does not by itself imply commutation. For rational sphere maps of degrees at least two, commutation does imply equality of their <Fatou sets> and <Julia sets>, by the <commuting rational maps of degree at least two have the same Julia set> theorem.
Back to article page
