ASYMPTOTICALLY AUTONOMOUS SEMIFLOWS - CHAIN RECURRENCE AND LYAPUNOV FUNCTIONS

被引：192

作者：

MISCHAIKOW, K ^{[1
]}

SMITH, H ^{[1
]}

THIEME, HR ^{[1
]}

机构：

[1] ARIZONA STATE UNIV,DEPT MATH,TEMPE,AZ 85287

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1995年 / 347卷 / 05期

关键词：

CHAIN RECURRENCE; ASYMPTOTICALLY AUTONOMOUS SEMIFLOW; LYAPUNOV FUNCTION;

D O I：

10.2307/2154964

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

From the work of C. Conley, it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set. Here, we improve a result of L. Markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow. In the special case that there is a Lyapunov function for the limiting semiflow, sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the Lyapunov function.

引用

页码：1669 / 1685

页数：17

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