Criteria for extension of commutativity to fractional iterates of holomorphic self-maps in the unit disc

Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk

Let $\phi$ be a univalent non-elliptic self-map of the unit disc $\mathbb{D}$ and let $({\psi }_t)$ be a continuous one-parameter semigroup of holomorphic functions in $\mathbb{D}$ such tha…