ASYMPTOTICALLY AUTONOMOUS SEMIFLOWS - CHAIN RECURRENCE AND LYAPUNOV FUNCTIONS

被引：190
|
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
收藏
页码：1669 / 1685
页数：17
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