Substitution Hamiltonians with bounded trace map orbits
type: Item
instance of: scholarly article
title: Substitution Hamiltonians with bounded trace map orbits
zbMATH Open document ID: 0996.37011
author: David Damanik
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-11-20T00:00:00Z
review text: This paper is devoted to discrete one-dimensional Schrödinger operators with aperiodic potentials generated by primitive invertible substitutions on a two-letter alphabet and their spectral properties. The author exhibits a class of substitution Hamiltonians with a zero-measure spectrum and uses the well-known Rohert's results on the trace map dynamics. As an application he presents a class of models exhibiting a purely singular continuous spectrum with probability one.
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 1533174
zbMATH Keywords: discrete one-dimensional Schrödinger operators
zbMATH Keywords: aperiodic potentials
zbMATH Keywords: substitution Hamiltonians
zbMATH Keywords: trace map dynamics
zbMATH Keywords: singular continuous spectrum
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6876
OpenAlex ID: W2087680163
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DOI: 10.1006/JMAA.2000.6876
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description: scientific article; zbMATH DE number 1533174