2024/12/22 by Lirui Feng, Feng, Lirui
Mathematics · #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2412.17071
openalex publication_date 2024/12/22 · openalex created_date 2024/12/25 · openalex updated_date 2026/07/28
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.