Iteration of order preserving subhomogeneous maps on a cone

Marianne Akian, Stéphane Gaubert, Bas Lemmens, Roger Nussbaum

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

We investigate the iterative behaviour of continuous order preserving subhomogeneous maps $f: K → K$, where $K$ is a polyhedral cone in a finite dimensional vector space. We show that each bounded orbit of $f$ converges to a periodic orbit and, moreover, the period of each periodic point of $f$ is bounded by equation given where $N$ is the number of facets of the polyhedral cone. By constructing examples on the standard positive cone in ℝ n, we show that the upper bound is asymptotically sharp. These results are an extension of work by Lemmens and Scheutzow concerning periodic orbits in the interior of the standard positive cone in ℝ n.

Original languageEnglish (US)
Pages (from-to)157-176
Number of pages20
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume140
Issue number1
DOIs
StatePublished - Jan 1 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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