Finite orbits in multivalued maps and Bernoulli convolutions
type: Item
instance of: scholarly article
title: Finite orbits in multivalued maps and Bernoulli convolutions
zbMATH Open document ID: 1382.37007
author: Christoph Bandt
published in: Advances in Mathematics
publication date: 2017-12-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1509.08672
review text: Here two related themes are studied. The first is the existence of network-like orbits arising in multi-valued maps, where orbits naturally have the structure of a branching tree, and a finite orbit has the structure of a tree with branches leading back to lower levels. The second concerns the classical topic of Bernoulli convolutions (these are examples of self-similar measures with overlaps) determined by a numerical parameter. The connection is via a natural map on the interval which is two-valued on the overlap region for the Bernoulli convolution. Here examples of points with specific combinatorial properties are found which are neither Pisot nor Salem numbers.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 11K16
zbMATH DE Number: 6817472
zbMATH Keywords: Bernoulli convolution
zbMATH Keywords: self-similar measure
zbMATH Keywords: multivalued map
zbMATH Keywords: symbolic dynamical system
MaRDI profile type: Publication
OpenAlex ID: W2962774863
arXiv ID: 1509.08672
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DOI: 10.1016/J.AIM.2017.11.011
description: scientific article