# Holomorphic motions commuting with semigroups

Studia Mathematica (1996)

- Volume: 119, Issue: 1, page 1-16
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topSłodkowski, Zbigniew. "Holomorphic motions commuting with semigroups." Studia Mathematica 119.1 (1996): 1-16. <http://eudml.org/doc/216283>.

@article{Słodkowski1996,

abstract = {A holomorphic family $f_z$, |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms $F_z$, |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions $F_z$ which, in addition, commute with some holomorphic families of holomorphic endomorphisms of $ℂ̅̅̅̅̅̅ \ f_z(E)$, |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.},

author = {Słodkowski, Zbigniew},

journal = {Studia Mathematica},

keywords = {holomorphic motion},

language = {eng},

number = {1},

pages = {1-16},

title = {Holomorphic motions commuting with semigroups},

url = {http://eudml.org/doc/216283},

volume = {119},

year = {1996},

}

TY - JOUR

AU - Słodkowski, Zbigniew

TI - Holomorphic motions commuting with semigroups

JO - Studia Mathematica

PY - 1996

VL - 119

IS - 1

SP - 1

EP - 16

AB - A holomorphic family $f_z$, |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms $F_z$, |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions $F_z$ which, in addition, commute with some holomorphic families of holomorphic endomorphisms of $ℂ̅̅̅̅̅̅ \ f_z(E)$, |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.

LA - eng

KW - holomorphic motion

UR - http://eudml.org/doc/216283

ER -

## References

top- [BR] L. Bers and H. L. Royden, Holomorphic families of injections, Acta Math. 157 (1986), 259-286. Zbl0619.30027
- [Bi] E. Bishop, Mappings of partially analytic spaces, Amer. J. Math. 83 (1961), 209-242. Zbl0118.07701
- [DH] A. Douady et J. Hubbard, Itération de polynômes quadratiques complexes, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), 123-126. Zbl0483.30014
- [EF] C. J. Earle and R. S. Fowler, Holomorphic families of open Riemann surfaces, Math. Ann. 270 (1985), 249-273. Zbl0537.30036
- [EKK] C. J. Earle, I. Kra and S. L. Krushkal, Holomorphic motions and Teichmüller spaces, Trans. Amer. Math. Soc. 343 (1994), 927-948. Zbl0812.30018
- [GR] R. C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, N.J., 1965. Zbl0141.08601
- [Ma] B. Maskit, Kleinian Groups, Springer, 1988.
- [MSS] R. Mañé, P. Sad and D. Sullivan, On the dynamics of rational maps, Ann. Sci. Ecole Norm. Sup. 16 (1983), 193-217. Zbl0524.58025
- [Mu] C. McMullen, Private letter, 1990.
- [Sł1] Z. Słodkowski, Holomorphic motions and polynomial hulls, Proc. Amer. Math. Soc. 111 (1991), 347-355. Zbl0741.32009
- [Sł2] Z. Słodkowski, Invariant extensions of holomorphic motions, abstract No. 873-30-234, Abstracts Amer. Math. Soc. 13 (1992), p. 259.
- [Sł3] Z. Słodkowski, Extensions of holomorphic motions, Ann. Scuola Norm. Sup. Pisa, to appear.
- [Su] D. Sullivan, Quasiconformal homeomorphisms and dynamics, III: Topological conjugacy classes of analytic endomorphisms, preprint, 1985.
- [ST] D. Sullivan and W. P. Thurston, Extending holomorphic motions, Acta Math. 157 (1986), 243-257. Zbl0619.30026

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.