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Manifolds which do not Admit Anosov Diffeomorphisms

Published online by Cambridge University Press:  22 January 2016

Kenichi Shiraiwa
Kenichi Shiraiwa*
Affiliation:
Nagoya University
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In [3], M. W. Hirsch obtained some necessary conditions for the existence of an Anosov diffeomorphism on a differentiable manifold. As an application, he constructed many manifolds which do not admit Anosov diffeomorphisms.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 49 , March 1973 , pp. 111 - 115
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Arkowitz, M.-Curjel, C. R.: Groups of Homotopy Classes, Lecture Notes in Mathematics, Springer Verlag, Berlin (1964).CrossRefGoogle Scholar
[2] Franks, J.: Anosov Diffeomorphisms, Proc. Symp. Pure Mathematics XIV, Global Analysis, Amer. Math. Soc, Province, R.I. (1970).Google Scholar
[3] Hirsch, M. W.: Anosov Maps, Polycyclic Groups and Homology, Topology 10 (1971), 177–183.Google Scholar
[4] Smale, S.: Differentiable Dynamical Systems, Bull. Amer. Math. Soc. 73 (1967), 747–817.Google Scholar