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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…
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…
Centralizers of non-elliptic univalent self-maps and the embeddability problem in the unit disc
Manuel D. Contreras, Santiago Díaz-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 of the…