Commuting holomorphic functions and hyperbolic automorphisms
Commuting holomorphic functions and hyperbolic automorphisms
We give a complete classification of the holomorphic self-maps of the unit ball of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper C Superscript n"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">C</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbf {C}^{n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> into itself which commute with a given hyperbolic automorphism.