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引用次数: 0
摘要
我们考虑一种光滑半流，它相对于巴拿赫空间上的秩为 k 的锥体具有强聚焦单调性。我们得到了它的一般动力学，即初始数据来自任意开放有界集的开放致密子集的半流要么是伪有序的，要么收敛于均衡。对于 \(k=1\) 的情况，就是著名的赫希通用收敛定理。对于 \(k=2\)的情况，我们得到的是通用的波恩卡-本迪克森定理（Poincaré-Bendixson Theorem）。
Semiflows Strongly Focusing Monotone with Respect to High-Rank Cones: I. Generic Dynamics
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 open bounded set either are 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 Poincaré-Bendixson Theorem.
期刊介绍：
Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.
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