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The topological stability of diffeomorphisms

Published online by Cambridge University Press:  22 January 2016

Kazumine Moriyasu
Kazumine Moriyasu*
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-03, Japan
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The present paper is concerned with the stability of diffeomorphisms of C∞ closed manifolds. Let M be a C∞ closed manifold and Diffr(M) be the space of Cr diffeomorphisms of M endowed with the Cr topology (in this paper we deal with only the case r = 0 or 1). Let us define

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 123 , September 1991 , pp. 91 - 102
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[ 1 ] Aoki, N., On homeomorphisms with pseudo orbit tracing property, Tokyo J. Math., 6 (1983), 329–334.CrossRefGoogle Scholar
[ 2 ] Aoki, N., The set of Axiom A diffeomorphisms with no cycle, preprint.CrossRefGoogle Scholar
[ 3 ] Franks, J., Necessary conditions for stability of diffeomorphisms, Trans. A.M.S., 158 (1971), 301–308.CrossRefGoogle Scholar
[ 4 ] Hirsch, M. and Pugh, C., Stable manifolds and hyperbolic sets, in Global Analysis, Proc. Sympos. Pure Math., A.M.S., 14 (1970), 133–163.CrossRefGoogle Scholar
[ 5 ] Mañé, R., A proof of the C1 stability conjecture, Publ. Math. I.H.E.S., 66 (1987), 161–210.Google Scholar
[ 6 ] Morimoto, A., Stochastically stable diffeomorphisms and Takens conjecture, Suriken Kokyuroku, 303 (1977), 8–24.Google Scholar
[ 7 ] Nitecki, Z., On semi-stability for diffeomorphisms, Invent. Math., 14 (1971), 83–122.CrossRefGoogle Scholar
[ 8 ] Nitecki, Z. and Shub, M., Filtrations, decompositions and explosions, Amer. J. Math., 97 (1976), 1029–1047.CrossRefGoogle Scholar
[ 9 ] Palis, J., On the C1 Ω-stability conjecture, Publ. Math. I.H.E.S., 66 (1987), 211–215.Google Scholar
[10] Peixoto, M., Structural stability on two-dimensional manifolds, Topology, 1 (1962), 101–120.CrossRefGoogle Scholar
[11] Robinson, C., Cr structural stability implies Kupka-Smale, In: Dynamical Systems, edited by Peixoto. Academic Press (1973).Google Scholar
[12] Robinson, C., Stability theorems and hyperbolicity in dynamical systems, Rocky Mountain J. Math., 7 (1977), 425–437.CrossRefGoogle Scholar
[13] Smale, S., The Ω-stability theorem, in Global Analysis, Proc. Sympos. Pure Math., A.M.S., 14 (1970), 289–297.Google Scholar
[14] Walters, P., Anosov diffeomorphisms are topologically stable, Topology, 9 (1970), 71–78.CrossRefGoogle Scholar
[15] Walters, P., On the pseudo-orbit tracing property and its relationship to stability, Springer L.N., No. 668 (1979), 231–244.Google Scholar