Article (Scientific journals)
A remark on Schröder's equation: Formal and analytic linearization of iterative roots of the power series f(z)=z
Reich, Ludwig; Tomaschek, Jörg
In pressIn Monatshefte für Mathematik
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Keywords :
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.
Disciplines :
Mathematics
Author, co-author :
Reich, Ludwig
Tomaschek, Jörg ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
A remark on Schröder's equation: Formal and analytic linearization of iterative roots of the power series f(z)=z
Publication date :
In press
Journal title :
Monatshefte für Mathematik
ISSN :
1436-5081
Publisher :
Springer, Vienna, Austria
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 05 May 2014

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