Eigenvectors of homogeneous order-bounded order-preserving maps

Horst R. Thieme

doi:10.3934/dcdsb.2017053

Article Contents

2017, Volume 22, Issue 3: 1073-1097. Doi: 10.3934/dcdsb.2017053

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Eigenvectors of homogeneous order-bounded order-preserving maps

Horst R. Thieme

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, USA

Author Bio: E-mail address: hthieme@asu.edu

Received: September 2015

Revised: May 2016

Published: September 2017

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Abstract

The existence of eigenvectors associated with the cone spectral radius is shown for homogenous, order-preserving, continuous maps that have compact and order-bounded powers (iterates). The order-boundedness makes it possible to show the existence of eigenvectors for perturbations of the maps using Hilbert's projective metric, while the power compactness or similar compactness properties together with a uniform continuity condition let the eigenvectors of the perturbations converge to an eigenvector of the original map.

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Mathematics Subject Classification: Primary:47H07, 47J10;Secondary:47N60.

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