Explosions in completely unstable flows. I. Preventing explosions

Nitecki, Zbigniew

doi:10.1090/S0002-9947-1978-0511399-2

Explosions in completely unstable flows. I. Preventing explosions
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by Zbigniew Nitecki

Trans. Amer. Math. Soc. 245 (1978), 43-61

DOI: https://doi.org/10.1090/S0002-9947-1978-0511399-2

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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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