Semiflows strongly focusing monotone with respect to high-rank cones. I: Generic dynamics
Dynamical Systems
2023-04-07 v2
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.
Keywords
Cite
@article{arxiv.2303.09691,
title = {Semiflows strongly focusing monotone with respect to high-rank cones. I: Generic dynamics},
author = {Lirui Feng},
journal= {arXiv preprint arXiv:2303.09691},
year = {2023}
}