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Transactions of the American Mathematical Society

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Explosions in completely unstable flows. I. Preventing explosions

Author: Zbigniew Nitecki
Journal: Trans. Amer. Math. Soc. 245 (1978), 43-61
MSC: Primary 58F10
MathSciNet review: 511399
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Abstract: Several conditions are equivalent to the property that a flow (on an open manifold) and its $ {C^0}$ perturbations have only wandering points. These conditions are: (i) there exists a strong Liapunov function; (ii) there are no generalized recurrent points in the sense of Auslander; (iii) there are no chain recurrent points, in the sense of Conley; (iv) there exists a fine sequence of filtrations; (v) relative to some metric; the flow is the gradient flow of a function without critical points. We establish these equivalences, and consider a few questions related to structural stability when all orbits wander.

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Keywords: Completely unstable flow, $ \Omega $-explosion, chain recurrence, generalized recurrence, prolongation, gradient flow, Liapunov function, filtration, structural stability
Article copyright: © Copyright 1978 American Mathematical Society

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