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Fixed points of certain Anosov maps on Riemannian manifolds

Published online by Cambridge University Press:  21 July 2009

TOMOO YOKOYAMA
TOMOO YOKOYAMA*
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro, Tokyo 153-8914, Japan (email: [email protected])
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Abstract

We present sufficient conditions for Anosov-type maps on Lie groups or Riemannian manifolds to have fixed points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 4 , August 2010 , pp. 1261 - 1270
Copyright
Copyright © Cambridge University Press 2009

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References

[1]Franks, J.. Anosov diffeomorphisms on tori. Trans. Amer. Math. Soc. 145 (1969), 117–124.CrossRefGoogle Scholar
[2]Franks, J.. Anosov diffeomorphisms. Global Analysis (Proceedings of Symposia in Pure Mathematics, XIV, Berkeley, CA, 1968). American Mathematical Society, Providence, RI, 1970, pp. 61–93.CrossRefGoogle Scholar
[3]Kawakubo, K.. The Theory of Transformation Groups. Oxford University Press, Oxford, 1991.CrossRefGoogle Scholar
[4]Manning, A.. There are no new Anosov diffeomorphisms on tori. Amer. J. Math. 96 (1974), 422–429.CrossRefGoogle Scholar
[5]Milnor, J.. Morse Theory (Annals of Mathematics Studies, 51). Princeton University Press, Pinceton, NJ, 1963.CrossRefGoogle Scholar
[6]Shiraiwa, K.. Some conditions on Anosov diffeomorphisms. Manifolds (Proceedings of the International Conference, Tokyo, 1973). University of Tokyo Press, Tokyo, 1975, pp. 205–209.Google Scholar
[7]Smale, S.. Differentiable dynamical system. Bull. Amer. Math. Soc. 73 (1966), 491–496.Google Scholar
[8]Sondow, J. D.. Fixed points of Anosov diffeomorphisms of certain manifolds. Notices Amer. Math. Soc. 17 (1970), 414.Google Scholar
[9]Sondow, J. D.. Fixed points of Anosov maps of certain manifolds. Proc. Amer. Math. Soc. 61(2) (1976), 381–384.CrossRefGoogle Scholar
[10]Sugiura, M.. Theory of Lie Groups. Kyoritsu Shuppan, Tokyo, 2000 (in Japanese).Google Scholar