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988 t,. E. KLOEDEN ANDJ. LORENZ forall ->0andall Xo A. Ifin additionthere exists a8o>0andforeach e>0atime T(e)>0 suchthat dist (x(t; Xo),A)<e forall >-T(e) wheneverdist(Xo,A)<o,wesaythat Ais uniformly asymptotically stable for (2.1). Lyapunov functions maybe used to characterize the stability of an arbitrarily shapedAforwhichthere is nosimple spectral theoryas whenAis asingletonset.
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