Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-15T02:06:03.502Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Cartwright, M. L.Almost periodic solutions of systems of two periodic equations. Presented at the Symposium on Nonlinear Vibrations(Kiev,1961). (To appear.)Google Scholar
(2)Gottschalk, W. H.Minimal sets: an introduction to topologicaldynamics. Bull. American Math. Soc. 64 (1958), 336–351Google Scholar
(3)Hall, D. W. and Spencer, G. L.Elementary topology (John Wiley; New York, 1955).Google Scholar
(4)Lefschetz, S.Liapunov and stability in dynamical systems. Bol. Soc. Mat. Mexicana, 3 (1958), 25–39Google Scholar