Using a result due to M. Shub, a theorem about the existence of fixed points inside the unit disc for extensions of expanding maps defined on the boundary is established. An application to a special class of rational maps on the Riemann sphere and some considerations on ergodic properties of these maps are also made.
Sulla base di un risultato di M. Shub, si dimostra un teorema riguardante la presenza di punti fissi all'interno del disco unitario per estensioni di funzioni espansive definite sul bordo. La Nota si conclude con un'applicazione ad una classe di funzioni razionali della sfera di Riemann e alcune considerazioni sulle proprietà ergodiche di tali funzioni.
@article{RLIN_1994_9_5_4_303_0,
author = {Roberto Tauraso},
title = {On fixed points of \( C^{1} \) extensions of expanding maps in the unit disc},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {5},
year = {1994},
pages = {303-308},
zbl = {0827.30022},
mrnumber = {1320582},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_1994_9_5_4_303_0}
}
Tauraso, Roberto. On fixed points of \( C^{1} \) extensions of expanding maps in the unit disc. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 5 (1994) pp. 303-308. http://gdmltest.u-ga.fr/item/RLIN_1994_9_5_4_303_0/
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