On simultaneous Abel equations
type: Item
instance of: scholarly article
title: On simultaneous Abel equations
zbMATH Open document ID: 0686.39009
DOI: 10.1007/BF01840002
author: Marek Cezary Zdun
published in: Aequationes Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137324
review text: The system (1) \(\phi [f(x)]=\phi (x)+1\quad \phi [g(x)]=\phi (x)+s\) is investigated, where x ranges over an open interval, and f and g are continuous commuting self-bijections of the interval. One would assume that then f and g are in some sense iterates of each other, and indeed the results are in that general direction. From the many results we (partially) quote: If \(\forall x\) \(f^ m(x)\neq g^ n(x)\) (m,n\(\in {\mathbb{Z}})\) whenever \(| m| +| n| \neq 0\) then there exists a unique s such that (1) has a continuous solution unique up to an additive constant. This solution is monotonic and s is irrational. The results are also applied to the problem of embedding two functions in a continuous iteration group.
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 4124293
zbMATH Keywords: simultaneous Abel equations
zbMATH Keywords: flows
zbMATH Keywords: iteration groups
zbMATH Keywords: system
zbMATH Keywords: continuous solution
zbMATH Keywords: continuous iteration group
MaRDI profile type: Publication
cites work: Q3714306
cites work: Q5592596
cites work: Sur les solutions de l'équation de translation
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cites work: Note on commutable functions
description: scientific article; zbMATH DE number 4124293