Morse -小不等式和Chafee - Infante吸引子

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Regular and Chaotic Dynamics Pub Date : 2022-12-10 DOI:10.1134/S156035472206003X

Leonardo Pires

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引用次数: 0

摘要

本文讨论标量Chafee - Infante方程的吸引子\(\mathcal{A}^{\lambda}\)的形状。我们在圆盘\(\mathbb{D}^{k}\)上构造了一个与Chafee - Infante方程的无限维动力学拓扑等价的Morse - small向量场。因此，我们利用Morse - small不等式得到了\(\mathcal{A}^{\lambda}\)的几何性质。

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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Morse – Smale Inequalities and Chafee – Infante Attractors

In this paper, we are concerned with the shape of the attractor \(\mathcal{A}^{\lambda}\) of the scalar Chafee – Infante equation. We construct a Morse – Smale vector field in the disk \(\mathbb{D}^{k}\) topologically equivalent to infinite-dimensional dynamics of the Chafee – Infante equation. As a consequence, we obtain geometric properties of \(\mathcal{A}^{\lambda}\) using the Morse – Smale inequalities.

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.

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