Explosions in completely unstable flows. I. Preventing explosions
Author:
Zbigniew Nitecki
Journal:
Trans. Amer. Math. Soc. 245 (1978), 4361
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 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197805113992
PII:
S 00029947(1978)05113992
Keywords:
Completely unstable flow,
explosion,
chain recurrence,
generalized recurrence,
prolongation,
gradient flow,
Liapunov function,
filtration,
structural stability
Article copyright:
© Copyright 1978
American Mathematical Society
