Semiflows strongly focusing monotone with respect to high-rank cones. I: Generic dynamics

Lirui Feng

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arXiv · 2303.09691

Semiflows strongly focusing monotone with respect to high-rank cones. I: Generic dynamics

Lirui Feng

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Abstract

We consider a smooth semiflow strongly focusing monotone with respect to a cone of rank k on a Banach space. We obtain its generic dynamics, that is, semiorbits with initial data from an open and dense subset of any bounded open set are either pseudo-ordered or convergent to an equilibrium. For the case k=1, it is the celebrated Hirsch's Generic Convergence Theorem. For the case k=2, we obtain the generic Poincare-Bendixson Theorem.

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Lirui Feng. 2023-03-16. Semiflows strongly focusing monotone with respect to high-rank cones. I: Generic dynamics. https://arxiv.org/abs/2303.09691

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