星体流动：通过 Lyapunov 函数进行表征

Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-06-10 DOI:10.1007/s00574-024-00403-w

Luciana Salgado

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摘要

在这项工作中，提出了基于 Lyapunov 函数的 $C^1$ 向量域的星属性特征。通过使用无穷小 Lyapunov 函数的概念，还获得了奇异集强同质性的条件。作为应用，我们得到了一些与流动的奇异双曲集相关的结果。

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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Star Flows: A Characterization Via Lyapunov Functions

In this work, it is presented a characterization of star property for a $C^1$ vector field based on Lyapunov functions. It is also obtained conditions to strong homogeneity for singular sets by using the notion of infinitesimal Lyapunov functions. As an application, we obtain some results related to singular hyperbolic sets for flows.

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Bulletin of the Brazilian Mathematical Society, New Series

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