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

• Autores: Brian Lins
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 1, 2007, págs. 157-164
• Idioma: inglés
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• Resumen

  • For a polyhedral domain , and a Hilbert metric nonexpansive map T:S?S which does not have a fixed point in S, we prove that the omega limit set ?(x;T) of any point x S is contained in a convex subset of the boundary ?S. 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