On holomorphic families of rational maps: finiteness, rigidity and stability
Shiga, Hiroshige
Kodai Math. J., Tome 24 (2001) no. 1, p. 48-65 / Harvested from Project Euclid
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We consider holomorphic families of rational maps from the viewpoint of complex dynamics. ¶ First, we consider some classes of families of rational maps which satisfy a certain stability condition. We show a finiteness theorem for such holomorphic families of rational maps parameterized by a Riemann surface of finite type. ¶ Next, we consider the monodromy of quasiconformally stable holomorphic families of rational maps over a punctured disk, and study the action of the monodromy on the Julia set.
Publié le : 2001-05-14
Classification:  37F45,  37F10,  37F15 
@article{1106157295,
     author = {Shiga, Hiroshige},
     title = {On holomorphic families of rational maps: finiteness, rigidity and stability},
     journal = {Kodai Math. J.},
     volume = {24},
     number = {1},
     year = {2001},
     pages = { 48-65},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1106157295}
}

Shiga, Hiroshige. On holomorphic families of rational maps: finiteness, rigidity and stability. Kodai Math. J., Tome 24 (2001) no. 1, pp.  48-65. http://gdmltest.u-ga.fr/item/1106157295/