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On existence of tolerance stable diffeomorphisms*

Published online by Cambridge University Press:  22 January 2016

Gikō Ikegami
Gikō Ikegami*
Affiliation:
Department of Mathematics, Faculty of General Education, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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We consider a compact smooth manifold M. Diff1 (M) denotes the space of C 1-diffeomorphisms of M onto itself with the usual C 1-topology. In the research of the qualitative theory of dynamical systems there is a desire to find a concept of stability of geometric global structure of orbits such that this stable systems are dense in the space of dynamical systems on M. Structural stability does not satisfy the density condition in Diff1 (M). Tolerance stability (see Section 2 for definition) is a candidate for the density property [7, p. 294]. Concerning tolerance stability there are researches as [6], [7], [8], and [2].

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 90 , June 1983, pp. 63 - 76
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

Footnotes

*

The author is partly supported by Grant in Aid for Scientific Research Project No. 546004.

References

[ 1 ] Irwin, M. C., Smooth dynamical systems, Academic press, 1980.Google Scholar
[ 2 ] Morimoto, A., The method of pseudo-orbit tracing and stability of dynamical systems, Seminar Note 39, Dept. of Math. Tokyo Univ., 1979, (in Japanese).Google Scholar
[ 3 ] Palis, J. and Smale, S., Structural stability theorems, Proceedings of symposia in pure math. (Global Analysis), Amer. Math. Soc, 14 (1970), 223–231.Google Scholar
[ 4 ] Robinson, C., Structural stability of C1 diffeomorphisms, J. Differential Equations, 22 (1976), 28–73.CrossRefGoogle Scholar
[ 5 ] Smale, S., Morse inequalities for a dynamical system, Bull. Amer. Math. Soc, 66 (1960), 43–49.CrossRefGoogle Scholar
[ 6 ] Takens, F., On Zeeman’s tolerance stability conjecture, Manifolds-Amsterdam 1970, Lecture Notes in Math., Springer, 197 (1971), 209–219.Google Scholar
[ 7 ] Takens, F., Tolerance stability, Dynamical Systems-Warwick 1974. Proceedings 1973/74 (Edited by Manning, A.), Lecture Notes in Math., Springer, 468 (1975), 293–304.Google Scholar
[ 8 ] White, W., On the tolerance stability conjecture, Dynamical systems (Edited by Peixoto, M.), Academic Press, 1973, 663–665.Google Scholar