A remark on Schröder's equation: Formal and analytic linearization of iterative roots of the power series f(z)=z

Reference : A remark on Schröder's equation: Formal and analytic linearization of iterative roots...


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/16566

Title :	A remark on Schröder's equation: Formal and analytic linearization of iterative roots of the power series f(z)=z
Language :	English
Author, co-author :	Reich, Ludwig []
	Tomaschek, Jörg [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	In press
Journal title :	Monatshefte für Mathematik
Publisher :	Springer
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	0026-9255
e-ISSN :	1436-5081
City :	Vienna
Country :	Austria
Keywords :	[en] Schröder equation ; Linearization ; Normal forms
Abstract :	[en] We study Schröder’s equation (i.e. the problem of linearization) for local analytic functions F with F (0)=0, F(0)=1, F(0) a root of 1. While Schröder’s equation in this case need not have even a formal solution, we show that if F is formally linearizable, then it can also be linearized by an invertible local analytic transformation. On the other hand, there exist also divergent series solutions of Schröder’s equation in this situation. We give some applications of our results to iterative functional equations, functional-differential equations and iteration groups.
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/16566
DOI :	10.1007/s00605-013-0601-3
Other URL :	http://download.springer.com/static/pdf/357/art%253A10.1007%252Fs00605-013-0601-3.pdf?auth66=1399470256_3eb6b0fdcc7012481afbe852e6f389be&ext=.pdf

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