Shift-maximal sequences in function iteration: Existence, uniqueness and multiplicity
type: Item
instance of: scholarly article
title: Shift-maximal sequences in function iteration: Existence, uniqueness and multiplicity
zbMATH Open document ID: 0657.58019
DOI: 10.1016/0022-247X(86)90001-6
author: R. Daniel Mauldin
author: William A. Beyer
author: Paul R. Stein
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: Shift-maximal sequences over two symbols arise in the theory of symbolic dynamics of the iteration of one-dimensional one parameter unimodal transformations \(\lambda\) F(x) for \(\lambda\in (0,1)\). Each sequence \({\mathbb{P}}\) may be associated with none, one, or more than one value of the parameter \(\lambda\). We call these values of \(\lambda\) : \(\lambda_{{\mathbb{P}}}\). We review previous theories of these sequences and prove, under certain conditions on F, the existence and uniqueness of \(\lambda_{{\mathbb{P}}}\). We discuss the theory of multiplicity of the \(\lambda_{{\mathbb{P}}}'s\) and give examples. We also discuss a generalized shift-maximal sequence structure and illustrate quadratic convergence in period doubling, different from Feigenbaum's geometric convergence. Finally, we review some of the experimental observations of shift-maximal sequences.
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 28D99
zbMATH DE Number: 4074011
zbMATH Keywords: Shift-maximal sequences
zbMATH Keywords: symbolic dynamics
zbMATH Keywords: iteration
zbMATH Keywords: period doubling
describes a project that uses: MACSYMA
MaRDI profile type: Publication
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full work available at URL: 0022-247x(86)90001-6
OpenAlex ID: W2028117064
description: scientific article; zbMATH DE number 4074011