具有无限延迟和双曲性的方程的循环

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-17 DOI:10.1016/j.nonrwa.2024.104221

Luís Barreira , Matheus G.C. Cunha , Claudia Valls

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引用次数: 0

摘要

我们证明，用指数二分法的存在性来表示具有无限延迟的线性延迟-差分方程的双曲性，完全可以用从方程的解中得到的线性环的双曲性来表征。作为对这一特征的应用，我们得到了几个结果：将双曲性扩展到不变簇中的所有方程；在足够小的线性扰动下，不变簇中所有方程的双曲性存在的稳健性；不变簇中所有谱的相等性；以及从有界扰动到有界解的可接受性特征来描述不变簇中所有方程的双曲性。

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Cocycles for equations with infinite delay and hyperbolicity

We show that the hyperbolicity of a linear delay-difference equation with infinite delay, expressed in terms of the existence of an exponential dichotomy, can be completely characterized by the hyperbolicity of a linear cocycle obtained from the solutions of the equation. As an application of this characterization, we obtain several consequences: the extension of hyperbolicity to all equations in the invariant hull; the robustness of the existence of hyperbolicity for all equations in this hull under sufficiently small linear perturbations; the equality of all spectra in the invariant hull; and a characterization of hyperbolicity for all equations in the invariant hull in terms of an admissibility property taking bounded perturbations to bounded solutions.

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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.