Eigenvectors of homogeneous order-bounded order-preserving maps

Research output: Contribution to journalArticle

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1073-1097
Number of pages25
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume22
Issue number3
DOIs
StatePublished - May 1 2017

Keywords

  • Collatz-Wielandt numbers
  • Cone spectral radius
  • Homogeneous map
  • Krein-Rutman theorem
  • Nonlinear eigenvectors
  • Ordered normed vector space
  • Population models with mating
  • Power compactness

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Eigenvectors of homogeneous order-bounded order-preserving maps'. Together they form a unique fingerprint.

  • Cite this