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A Denjoy–Wolff theorem for Hilbert metric nonexpansive maps on polyhedral domains

Published online by Cambridge University Press:  01 July 2007

BRIAN LINS
BRIAN LINS*
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, U.S.A. e-mail: bclins@math.rutgers.edu
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Abstract

For a polyhedral domain , and a Hilbert metric nonexpansive map T:Σ→Σ which does not have a fixed point in Σ, we prove that the omega limit set ω(x;T) of any point x ∈ Σ is contained in a convex subset of the boundary ∂Σ. We also identify a class of order-preserving homogeneous of degree one maps on the interior of the standard cone which demonstrate that there are Hilbert metric nonexpansive maps on an open simplex with omega limit sets that can contain any convex subset of the boundary.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 157 - 164
Copyright
Copyright © Cambridge Philosophical Society 2007

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