Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-24T05:02:29.618Z Has data issue: false hasContentIssue false

Notes on Lyapunov graphs and non-singular Smale flows on three manifolds

Published online by Cambridge University Press:  22 January 2016

Nobuatsu Oka*
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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.

In the 1980s, Franks, Pugh and Shub raised the question “Given any subshift of finite type σA: ΣA → ΣA is there a non-singular Smale flow (or an NS flow for short) on S3 with the suspension of σA as a basic set?” (See [5] and [12]).

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[1] Bowen, R., One dimensional hyperbolic set for flows, J. Differential Equations, 12 (1972),173179.Google Scholar
[2] Birman, J. and Williams, R. F., Knotted periodic orbits in dynamical system II: knot holders for fibered knots in Contemporary Mathematics, Low Dimensional Topology, Vol. 20, 1983.Google Scholar
[3] Franke, J. and Selgrade, J., Hyperbolicity and chain recurrence, J. Differential Equations, 26 (1977), 2736.Google Scholar
[4] Franks, J., Homology and Dynamical systems, C.B.M.S. Regional Conf. Series in Math., 49 Amer. Math. Soc. Providence R.I., 1982.Google Scholar
[5] Franks, J., Symbolic dynamics in flows on three manifold, Trans. Amer. Math. Soc., 279 (1983), 231236.Google Scholar
[6] Franks, J., Non-singular Smale flow on S 3 , Topology, 24 No. 3 (1985), 265282.Google Scholar
[7] Hempel, J., 3-manifolds, Ann. of Math. Studies No. 86, Princeton University press, Princeton N.J., 1976.Google Scholar
[8] Jaco, W., Lectures on three manifold topology C.B.M.S. Regional conf. Series in Math., 43 Amer. Math. Soc. Providence, R.I., 1980.Google Scholar
[9] Kim, P. K., Some 3-manifold which admit Klein bottles, Trans. Amer. Math. Soc., 244 (1978), 299312.Google Scholar
[10] Kobayashi, T., Primitive links of non-singular Morse-Smale flows on the special Seifert fiberd manifold, Topology Appl., 20 No. 1, (1985), 6778.Google Scholar
[11] Morgan, J., Non-Singular Morse Smale flows on 3-dimensional manifold, Topology, 18 (1978), 4153.Google Scholar
[12] Pugh, C. and Shub, M., Embedding suspension of subshifts of finite type in S 3 in Contributions to Geometry and Analysis, Percelli, C. and Sacksteder, R. eds., Johns Hopkins University Press, 1981.Google Scholar
[13] Rolfsen, D., Knots and Links, Publish or Perish Inc., Berkeley, 1976.Google Scholar
[14] Sasano, K., Links of closed orbits of non-singular Morse-Smale flows, Proc. Amer. Math. Soc., 88 (1983), 727734.Google Scholar
[15] Smale, S., Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 797817.Google Scholar
[16] Wada, M., Links which consist of the closed orbits of non-singular Morse-Smale flow on 3-sphere, preprint.Google Scholar