Geodesic
Holomorphic maps of the disk into itself with invariant diameter and bounded distortion
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2015), pp. 51-63

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We consider a problem of embeddability of holomorphic map of the unit disk into itself with invariant diameter and bounded distortion into one-parameter semigroup. Here we require that the elements of one-parameter semigroup have the same properties as the original map does. We obtain embeddability criteria, the solution is given in terms of the Königs function.
Keywords: one-parameter semigroup, fractional iterates, infinitesimal generator, Königs function, fixed points. 
@article{IVM_2015_8_a4,
     author = {O. S. Kudryavtseva},
     title = {Holomorphic maps of the disk into itself with invariant diameter and bounded distortion},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {51--63},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_8_a4/}
}
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O. S. Kudryavtseva. Holomorphic maps of the disk into itself with invariant diameter and bounded distortion. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2015), pp. 51-63. http://geodesic.mathdoc.fr/item/IVM_2015_8_a4/