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Topological stability of solenoidal automorphisms

Published online by Cambridge University Press:  22 January 2016

Nobuo Aoki
Nobuo Aoki*
Affiliation:
Tokyo Metropolitan University, Department of Mathematics, Tokyo, Japan
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In [10] A. Morimoto proved that every topologically stable homeomorphism of a compact manifold M has the pseudo-orbit tracing property in the case dim (M) ≥ 2. Further, in studying relation between the topological stability and other stability of diffeomorphisms, he showed the following

Theorem A. Let Rr be the r-dimensional vector group and φ be a group automorphism of Rr.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 90 , June 1983 , pp. 119 - 135
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[ 1 ] Aoki, N., A group automorphism is a factor of a direct product of a zero entropy and a Bernoulli automorphism, Fund. Math., 114 (1981), 159–171.Google Scholar
[ 2 ] Aoki, N., Dateyama, M. and Komuro, M., Solenoidal automorphisms with specification, Monatsh. Math., 93 (1982), 79–110.Google Scholar
[ 3 ] Aoki, N. and Dateyama, M., The OE-property of group automorphisms, (to appear in J. Math. Soc. Japan, 36).Google Scholar
[ 4 ] Bowen, R., Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math., 470, Berlin-Heiderberg-New York: Springer, 1975.Google Scholar
[ 5 ] Halmos, P. R. and Samelson, H., On monothetic groups, Proc. Nat. Acad. Sci. U.S.A., 28 (1942), 254–258.Google Scholar
[ 6 ] Lang, S., Algebra, Addison-Wesley, 1972.Google Scholar
[ 7 ] Kurosch, A. G., The Theory of Groups I and II, New York, Chelsea, 1960.Google Scholar
[ 8 ] Nitecki, Z. and Shub, M., Filtrations, decompositions and explosions, Amer. J. Math., 97 (1976), 1029–1047.Google Scholar
[ 9 ] Morimoto, A., Stochastically stable diffeomorphisms and Takens’s conjecture, (preprint)Google Scholar
[10] Morimoto, A., Stochastic stability of group automorphisms, (preprint)Google Scholar
[11] Morimoto, A., The method of the pseudo-orbit tracing property and stability, Tokyo Univ. Seminary notes 39, 1979 (Japanese)Google Scholar
[12] Pontrjagin, L., Topological Groups, Godon and Breach Science Publ. Inc., 1966.Google Scholar
[13] Yuzvinskii, S. A., Calculation of the entropy of a group endomorphism, Siberian Math. J., 8 (1967), 230–239.Google Scholar