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The gradient structure of a flow: I

Published online by Cambridge University Press:  10 December 2009

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Abstract

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Each flow dominates a unique gradient flow (the gradient part) which in turn dominates any other gradient flow dominated by the original flow. The set of points carried to rest points of the gradient part (the chain recurrent set) is characterized in terms of a recurrence relation. Filtrations of the given flow correspond to those of the gradient part.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Volume 8: Charles Conley Memorial Issue , December 1988 , pp. 11 - 26
Copyright
Copyright © Cambridge University Press 1988

Footnotes

†

The author was on leave from the University of Wisconsin at the time this paper was written.

References

REFERENCES

Auslander, J.. Generalized recurrence in dynamical systems. Contr. Differential Equations 3 (1964), 65–74.Google Scholar
Churchill, R.. Isolated invariant sets in compact metric spaces. J. Differential Equations.Google Scholar
Conley, C.. On the continuation of invariant sets of a flow. Proceedings of the International Congress of Mathematicians 1970. Gauthier-Villars, Paris (1971), 909–913.Google Scholar
Conley, C.. On a generalization of the Morse index. Proceedings of the NRC—MRC Conference on Ordinary Differential Equations, Washington, DC, June 1971. Academic Press, New York (1972), 27–33.Google Scholar
Conley, C.. Some abstract properties of the set of invariant sets of a flow. Illinois J. Math. 16 (1972), 663–668.Google Scholar
Conley, C. & Easton, R.. Isolated invariant sets and isolating blocks. Trans. Amer. Math. Soc. 158 (1971), 35–61.Google Scholar
Montgomery, J.. Some perturbation theorems for flows on a compact metric space. Thesis. University of Wisconsin (1971).Google Scholar