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 language | English (US) |
|---|---|
| Pages (from-to) | 1073-1097 |
| Number of pages | 25 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 22 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 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
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