Dilatations and continued fractions
type: Item
instance of: scholarly article
title: Dilatations and continued fractions
zbMATH Open document ID: 0758.15002
DOI: 10.1016/0024-3795(92)90051-B
author: Max Bauer
published in: Linear Algebra and its Applications
publication date: 1992-10-26T00:00:00Z
review text: A matrix is called a primitive irreducible matrix (or in the author's terms a Perron-Frobenius matrix) if it is entrywise nonnegative and some power is entrywise positive. The author's principal result shows how to express the spectral radius and corresponding (normalized) eigenvector of a class of primitive irreducible integer matrices as generalized continued fractions. This result is applied to a problem in topology involving pseudo-Anosov maps of hyperbolic surfaces.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15B36
zbMATH DE Number: 69529
zbMATH Keywords: dilatations
zbMATH Keywords: primitive irreducible matrix
zbMATH Keywords: Perron-Frobenius matrix
zbMATH Keywords: spectral radius
zbMATH Keywords: integer matrices
zbMATH Keywords: generalized continued fractions
zbMATH Keywords: pseudo-Anosov maps
zbMATH Keywords: hyperbolic surfaces
reviewed by: George Phillip Barker
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 69529