Semiflows Strongly Focusing Monotone with Respect to High-Rank Cones: I. Generic Dynamics

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-12 DOI:10.1007/s10884-024-10372-9

Lirui Feng

引用次数: 0

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 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.

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相对于高容锥强聚焦单调的半流：I. 一般动力学

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）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.