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Hyperbolic flows are topologically stable

Published online by Cambridge University Press:  17 April 2009

Sung Kyu Choi
Affiliation:
Department of Mathematics, Chungnam National University Taejon, 305–764, Korea
Jong Suh Park
Affiliation:
Department of Mathematics, Chungnam National University Taejon, 305–764, Korea
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Abstract

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We show that any hyperbolic flow (X, π) on a metric space X is topologically stable by showing that it is expansive and has the chain-tracing property.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bowen, R. and Walters, P., ‘Expansive one-parameter flows’, J. Differential Equations 12 (1972), 180193.CrossRefGoogle Scholar
[2]Hurley, M., ‘Consequences of topological stability’, J. Differential Equations 54 (1984), 6072.CrossRefGoogle Scholar
[3]Ombach, J., ‘Consequences of the pseudo orbits tracing property and expansiveness’, J. Austral. Math. Soc. 43 (1987), 301313.CrossRefGoogle Scholar
[4]Shub, M., Global stability of dynamical systems (Springer-Verlag, Berlin, Heidelberg, New York, 1987).CrossRefGoogle Scholar
[5]Thomas, R.F., ‘Stability properties of one-parameter flows’, Proc. London Math. Soc. 45 (1982), 479505.CrossRefGoogle Scholar