16 citations · 50 across the 29 of their papers we have counts for
35 papers
On generalized embeddability of a non-elliptic self-map
Manuel D. Contreras, Santiago D\'ıaz-Madrigal, Pavel Gumenyuk
We study the structure of the centralizer of a non-elliptic holomorphic self-map of the unit disc and its relation with continuous dynamical structures. We prove that if the identi…
Simultaneous linearization and centralizers of parabolic self-maps II: positive hyperbolic step
Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk
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…
Simultaneous linearization and centralizers of parabolic self-maps I: zero hyperbolic step
Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk
Let be a parabolic self-map of the unit disc having zero hyperbolic step. We study holomorphic self-maps of commuting with .…
Hyperbolic convexity of holomorphic level sets
Iason Efraimidis, Pavel Gumenyuk
We prove that the sublevel set , , is geodesically convex with resp…
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…
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 be a univalent non-elliptic self-map of the unit disc and let be a continuous one-parameter semigroup of holomorphic functions in such tha…