Skip to main content
×
Home
    • Aa
    • Aa

Gradient-like flows on 3-manifolds

  • K. A. de Rezende (a1)
Abstract
Abstract

In this paper, we determine properties that a Lyapunov graph must satisfy for it to be associated with a gradient-like flow on a closed orientable three-manifold. We also address the question of the realization of abstract Lyapunov graphs as gradient-like flows on three-manifolds and as a byproduct we prove a partial converse to the theorem which states the Morse inequalities for closed orientable three-manifolds. We also present cancellation theorems of non-degenerate critical points for flows which arise as realizations of canonical abstract Lyapunov graphs.

Copyright
References
Hide All
[B]Brakes W. R.. Sewing-up link exteriors. Low Dimensional Topology. London Mathematical Society Lecture Note Series 48. Bangor, 1979. pp 2737.
[C]Conley C.. Isolated Invariant Sets and the Morse Index. CBMS Regional Conf. Series in Math. 38. American Mathematical Society: Providence, RI, 1978.
[dR]de Rezende K.. Smale flows on the three-sphere. Trans. Amer. Math. Soc. 303 (1987), 283310.
[dR, F]de Rezende K. & Franzosa R.. Lyapunov graphs and flows on surfaces. Trans. Amer. Math. Soc. To appear.
[F1]Franks J.. Non-singular Smale flows on S 3. Topology 24 (1985), 265282.
[F2]Franks J.. Homology and Dynamical Systems. CBMS Regional Conf. Series in Math. 49. American Mathematical Society: Providence, RI, 1982.
[FKV]Fomenko A. T., Kuznetsov V. & Volodin I.. The problem of discriminating algorithmically the standard three-dimensional sphere. Russian Math. Surveys 29(5) (1974), 71172.
[H]Hempel J.. 3-Manifolds, Annals of Mathematical Studies 86. Princeton University Press: Princeton, 1976.
[M1]Milnor J.. Lectures on the h-cobordism Theorem. Princeton Mathematical Notes. Princeton University Press: Princeton, 1965.
[M2]Milnor J.. A unique decomposition theorem for 3-manifolds. Amer. J. Math. 84 (1962), 17.
[S1]Smale S.. On gradient dynamical systems. Ann. Math. 74 (1961), 199206.
[S2]Smale S.. Generalized Poincaré's Conjecture in dimensions greater than four. Ann. Math. 74 (1961), 391406.
[Sm]Smoller J.. Shock Waves and Reaction Diffusion Equations. Springer: Berlin, 1983.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 2 *
Loading metrics...

Abstract views

Total abstract views: 73 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd October 2017. This data will be updated every 24 hours.