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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 C1-diffeomorphisms of M onto itself with the usual C1-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].

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

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