On the Existence of Smooth Lyapunov Functions for Arbitrary Closed Sets

被引：0

作者：

Fathi, Albert ^{[1
,2
]}

机构：

[1] Georgia Inst Technol, Atlanta, GA 30332 USA

[2] ENS Lyon, Sch Math, Lyon, France

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2022年 / 53卷 / 03期

关键词：

Flow; Smooth Lyapunov; Converse Lyapunov; Isolating block;

D O I：

10.1007/s00574-022-00291-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a simpler proof of the existence of isolating blocks due to Conley and Easton (Trans Am Math Soc 158:35-61, 1983) based on a generalization of the work of Wilson Jr. and Yorke (J Differ Equ 13:106-123, 1973) on Lyapunov functions and isolating blocks. This will also yield a proof of Massera's (Ann Math 64:182-206, 1956) converse Lyapunov Theorem and a proof of a Theorem independently due to Duistermaat and Hormander (Acta Math 128:183-269, 1972) and Sullivan (Invent Math 36:225-255, 1976).

引用

页码：957 / 980

页数：24

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