# American Institute of Mathematical Sciences

May  2017, 22(3): 1073-1097. doi: 10.3934/dcdsb.2017053

## Eigenvectors of homogeneous order-bounded order-preserving maps

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

Received  September 2015 Revised  May 2016 Published  January 2017

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.

Citation: Horst R. Thieme. Eigenvectors of homogeneous order-bounded order-preserving maps. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 1073-1097. doi: 10.3934/dcdsb.2017053
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