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Main Author:	Feng, Lirui
Format:	Preprint
Published:	2024
Subjects:	Dynamical Systems
Online Access:	https://arxiv.org/abs/2412.17071
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author	Feng, Lirui
author_facet	Feng, Lirui
contents	We consider a semiflow strongly focusing monotone with respect to a cone of rank k on a Banach space. We prove that the omega-limit set of a pseudo-ordered semiorbit is ordered, which is called as pseudo-ordered principle. Based on this principle, we obtain the solid Poincar\{'}e-Bendixson theorem with the rank k=2, that is, the omega-limit set of a pseudo-ordered semiorbit is either a nontrivial periodic orbit or a set consisting of equilibria with their potential connected orbits. The generic solid dynamics theorem with a general rank k and the generic solid Poincar\{'}e-Bendixson theorem with the rank k=2 are also obtained.
format	Preprint
id	arxiv_https___arxiv_org_abs_2412_17071
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Semiflows strongly focusing monotone with respect to high-rank cones: II. Pseudo-ordered principle Feng, Lirui Dynamical Systems We consider a semiflow strongly focusing monotone with respect to a cone of rank k on a Banach space. We prove that the omega-limit set of a pseudo-ordered semiorbit is ordered, which is called as pseudo-ordered principle. Based on this principle, we obtain the solid Poincar\{'}e-Bendixson theorem with the rank k=2, that is, the omega-limit set of a pseudo-ordered semiorbit is either a nontrivial periodic orbit or a set consisting of equilibria with their potential connected orbits. The generic solid dynamics theorem with a general rank k and the generic solid Poincar\{'}e-Bendixson theorem with the rank k=2 are also obtained.
title	Semiflows strongly focusing monotone with respect to high-rank cones: II. Pseudo-ordered principle
topic	Dynamical Systems
url	https://arxiv.org/abs/2412.17071

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