Iteration of order preserving subhomogeneous maps on a cone

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dc.creatorAkian, Marianne
dc.creatorGaubert, Stephane
dc.creatorLemmens, Bas
dc.creatorNussbaum, Roger
dc.date2004-10-05
dc.date.accessioned2026-07-07T06:26:26Z
dc.date.available2026-07-07T06:26:26Z
dc.descriptionWe investigate the iterative behaviour of continuous order preserving subhomogeneous maps that map a polyhedral cone into itself. For these maps we show that every bounded orbit converges to a periodic orbit and, moreover, that there exists an a priori upper bound for the periods of periodic points that only depends on the number of facets of the polyhedral cone. By constructing examples on the standard positive cone, we show that the upper bound is asymptotically sharp. These results are an extension of recent work by Lemmens and Scheutzow concerning periodic orbits in the interior of the standard positive cone.
dc.description20 pages, AMSLaTeX. To appear in "Mathematical Proceedings of the Cambridge Philosophical Society"
dc.identifierhttps://arxiv.org/abs/math/0410084
dc.identifierhttp://arxiv.org/abs/math/0410084
dc.identifierMath. Proc. Camb. Phil. Soc. (2006), 140, pp. 157--176
dc.identifierdoi:10.1017/S0305004105008832
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97106
dc.subjectDynamical Systems
dc.subject54H20 (Primary), 47H07 (Secondary)
dc.titleIteration of order preserving subhomogeneous maps on a cone
dc.typetext

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