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Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions
Transactions of the American Mathematical Society
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 asymptoticallydoi:10.1090/s0002-9947-1995-1290727-7 fatcat:26mvpm2g7rb6xakar7jnxsktrm