TY - JOUR
T1 - Asymptotically autonomous semiflows
T2 - Chain recurrence and lyapunov functions
AU - Mischaikow, Konstantin
AU - Smith, Hal
AU - Thieme, Horst
PY - 1995/5
Y1 - 1995/5
N2 - 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.
AB - 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.
KW - Asymptotically autonomous semiflow
KW - Chain recurrence
KW - Lyapunov function
UR - http://www.scopus.com/inward/record.url?scp=0000703838&partnerID=8YFLogxK
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U2 - 10.1090/S0002-9947-1995-1290727-7
DO - 10.1090/S0002-9947-1995-1290727-7
M3 - Article
AN - SCOPUS:0000703838
SN - 0002-9947
VL - 347
SP - 1669
EP - 1685
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 5
ER -