Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-28T05:03:08.897Z Has data issue: false hasContentIssue false

Fixed points of certain Anosov maps on Riemannian manifolds

Published online by Cambridge University Press:  21 July 2009

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

Abstract

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

Type
Research Article
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Franks, J.. Anosov diffeomorphisms on tori. Trans. Amer. Math. Soc. 145 (1969), 117124.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. 6193.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), 422429.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. 205209.Google Scholar
[7]Smale, S.. Differentiable dynamical system. Bull. Amer. Math. Soc. 73 (1966), 491496.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), 381384.CrossRefGoogle Scholar
[10]Sugiura, M.. Theory of Lie Groups. Kyoritsu Shuppan, Tokyo, 2000 (in Japanese).Google Scholar