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Expansive flows and their centralizers

Published online by Cambridge University Press:  22 January 2016

Masatoshi Oka
Masatoshi Oka*
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Science University of Tokyo
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R. Bowen and P. Walters [2] have defined expansive flows on metric spaces which generalized the similar notion by D. Anosov [1]. On the other hand, P. Walters [4] investigated continuous transformations of metric spaces with discrete centralizers and unstable centralizers and proved that expansive homeomorphisms have unstable centralizers.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 64 , December 1976 , pp. 1 - 15
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Anosov, D. V.: Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math. 90 (1967).Google Scholar
[2] Bowen, R. and Walters, P.: Expansive One-parameter Flows, J. Differential Equations 12 (1972), 180–193.Google Scholar
[3] Kato, K. and Morimoto, A.: Topological stability of Anosov flows and their centralizers, Topology 12 (1973), 255–273.Google Scholar
[4] Walters, P.: Homeomorphisms with Discrete Centralizers and Ergodic Properties, Math. System Theory, Vol. 4, No. 4 (1970), 322–326.Google Scholar