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Hyperbolic nonwandering sets without dense periodic points

Published online by Cambridge University Press:  22 January 2016

Masahiro Kurata
Masahiro Kurata*
Affiliation:
Department of Mathematics, Faculty of Science Hokkaido University
*
Current Address: Department of Mathematics, Nagoya Institute of Technology
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In this paper we give a negative answer to the problem which is suggested in [3]: if a nonwandering set Ω is hyperbolic, are the periodic points dense in Ω?

Newhouse and Palis proved that on two dimensional closed manifolds the answer is positive ([1], [2]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 74 , July 1979 , pp. 77 - 86
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

[1] Newhouse, S. and Palis, J., Hyperbolic nonwandering sets on two-dimensional manifolds, Dynamical Systems, ed. Peixoto, M. M., Academic Press, 1973.Google Scholar
[2] Palis, J. and Pugh, C. C., Fifty problems in dynamical systems, Dynamical Systems—Warwick 1974, ed. Manning, A., Lecture Notes in Math., 468, Springer-Verlag, 1975.Google Scholar
[3] Smale, S., Differentiate dynamical systems, Bull. Amer. Math. Soc, 73 (1967), 747–817.Google Scholar