Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-29T07:04:33.034Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Properties of Anosov Flows

Published online by Cambridge University Press:  20 November 2018

W. Byers
W. Byers*
Affiliation:
Sir George Williams University, Montreal, Quebec
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Anosov flows are a generalization of geodesic flows on the unit tangent bundles of compact manifolds of negative sectional curvature. They were introduced and are dealt with at length by Anosov in [2]. Moreover they form an important class of examples of flows satisfying Smale's axioms A and B (see [15]). In that paper Smale poses the problem of determining which manifolds admit Anosov flows. In this paper we obtain information about the fundamental groups of such manifolds. These generalize results which have been obtained for the fundamental groups of manifolds of negative curvature (see Preissmann [13], Byers [6]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1114 - 1121
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Abraham, R. and Robbin, J., Transversal mappings and flows (Benjamin, New York, 1967).Google Scholar
2. Anosov, D. V., Geodesic flows on closed Riemannian manifolds of negative curvature, Proc. Steklov Inst, of Math. 90 (1967) (A.M.S. translation 1969).Google Scholar
3. Arnold, V. I. and Avez, A., Ergodic problems of classical mechanics (Benjamin, New York, 1968).Google Scholar
4. Avez, A., Anosov dijfeomorphisms, Topological dynamics (ed. Auslander, Gottschalk, Benjamin, 1968).Google Scholar
5. Bishop, R. L. and O'Neill, B., Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1–49.Google Scholar
6. Busemann, H., Spaces with non-positive curvature, Acta Math. 80 (1948), 259–310.Google Scholar
7. Byers, W., On a theorem of Preissmann, Proc. Amer. Math. Soc. 24 (1970), 50–51.Google Scholar
8. Franks, J., Anosov diffeomorphisms, Global Analysis, Proc. Symp. Pure Math., Vol. XIV, Amer. Math. Soc. (1970), 61–93.Google Scholar
9. Hirsch, M., Pugh, C., and Shub, M., Invariant manifolds (to appear).Google Scholar
10. Haefliger, A., Varietées Feuilletées, Ann. Scoula Norm. Sup. Pisa 16 (1962), 367–397.Google Scholar
11. Newhouse, S. E., Anosov diffeomorphisms, Amer. J. Math. 92 (1970), 761–770.Google Scholar
12. Novikov, S. P., Topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965), 248–278.Google Scholar
13. Preissmann, A., Quelques propriétés globales des expaces de Riemann, Comment. Math. Helv. 15 (1942-43), 175–216.Google Scholar
14. Reeb, G., Sur certaines propriétés topologiques des variétés feuillitées, Act. Se. et Ind. (Hermann, Paris, 1952).Google Scholar
15. Smale, S., Differentiable dynamical systems, Bull. Amer. Math. Soc. 78 (1967), 747–817.Google Scholar