P. Gumenyuk

activity

20242026

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6 papers · 1 filter

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

Hyperbolic convexity of holomorphic level sets

Iason Efraimidis, Pavel Gumenyuk

We prove that the sublevel set ${z \in D : k_{D} (z, z_{0}) - k_{D} (f (z), w_{0}) < I^¼}$ , $I^¼ \in R$ , is geodesically convex with re…

math.CV2024

Hyperbolic distortion and conformality at the boundary

Pavel Gumenyuk, Maria Kourou, Annika Moucha +1

We characterize two classical types of conformality of a holomorphic self-map of the unit disk at a boundary point - existence of a finite angular derivative in the sense of Carath…

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…

math.CV2024

Centralizers of non-elliptic univalent self-maps and the embeddability problem in the unit disc

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

The embeddability problem is a very old and hard problem in discrete holomorphic iteration which deals with determining general conditions on a given univalent self-map $I ¨ $ of the…