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On connexion, invariance and stability in certain flows

Published online by Cambridge University Press:  24 October 2008

D. Desbrow
D. Desbrow
Affiliation:
Trinity College, Cambridge
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Extract

1. Suppose that f is a homeomorphism of the Euclidean plane E2 onto itself. The set M ⊂ E2 is said to be invariant if f(M) = M and minimal if it is non-void, closed, invariant and irreducible with respect to these properties. In general, invariant and minimal sets in E2 can have a finite or infinite number of components.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 1 , January 1964 , pp. 51 - 55
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

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(4)Lefschetz, S.Liapunov and stability in dynamical systems. Bol. Soc. Mat. Mexicana, 3 (1958), 25–39Google Scholar