| Issue |
ESAIM: Proc.
Volume 46, November 2014
ECIT 2012, 19th European Conference on Iteration Theory
|
|
|---|---|---|
| Page(s) | 47 - 62 | |
| DOI | https://doi.org/10.1051/proc/201446005 | |
| Published online | 05 December 2014 | |
Recent results on iterative roots
Faculty of Mathematics, Computer
Science and Econometrics, University of Zielona Góra, Szafrana 4a,
PL-65-516
Zielona Góra,
Poland
e-mail: w.jarczyk@wmie.uz.zgora.pl
This is a rough survey of some results on iterative roots (fractional iterates) published recently. Also some historical information to clear the connection to previous results has been given. The main topics are: the conjugacy of piecewise monotonic functions and their iterative roots, stability of iterative roots, some substitutes and generalizations of the notion of iterative root using set-valued functions.
Résumé
Le présent article de revue approximative contient de certains résultats sur les racines itératives (itérées fractionnaires) publiés récemment. Une information historique est aussi donnée pour montrer la liason avec des résultats précédents. Les sujets principaux sont : la conjugaison des fonctions monotones par morceaux et leurs racines itératives, stabilité des racines itératives, certains substituts et généralizations de la notion de la racine itérative qui utilisent les fonctions multivaluées.
Mathematics Subject Classification: 3902, 39B12, 26A18 / 26A48, 54C60
Key words: iteration / iterative root / topological conjugacy / stability / piecewise monotonic function / set-valued function / formal power series / homeomorphism of the circle
Mots clés : itération / racine itrative / conjugaison topologique / stabilité / fonction monotone á morceaux / fonction multivaluée / série formelle / homéomorphisme du cercle
© EDP Sciences, SMAI 2014
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