M. D. Contreras

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math.CV2026

Simultaneous linearization and centralizers of parabolic self-maps II: positive hyperbolic step

Manuel D. Contreras, Santiago DÃaz-Madrigal, Santiago Díaz-Madrigal +1

The study of holomorphic self-mappings of the unit disc commuting under the composition goes back to A.L. Shields (1964), W.A. Pranger (1970), D.F. Behan (1973), and C.C. Cowen (19…

math.CV2025

Simultaneous linearization and centralizers of parabolic self-maps I: zero hyperbolic step

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

Let $I ¨ : D \to D$ be a parabolic self-map of the unit disc $D$ having zero hyperbolic step. We study holomorphic self-maps of $D$ commuting with $I ¨ $ …

math.CV2024

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

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

Let $I ¨ $ be a univalent non-elliptic self-map of the unit disc $D$ and let $(I ¨ _{t})$ be a continuous one-parameter semigroup of holomorphic functions in $D$ such t…