Skip to main content
    • Aa
    • Aa

Gradient-like flows on 3-manifolds

  • K. A. de Rezende (a1)

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.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[C] C. Conley . Isolated Invariant Sets and the Morse Index. CBMS Regional Conf. Series in Math. 38. American Mathematical Society: Providence, RI, 1978.

[dR] K. de Rezende . Smale flows on the three-sphere. Trans. Amer. Math. Soc. 303 (1987), 283310.

[F1] J. Franks . Non-singular Smale flows on S3. Topology 24 (1985), 265282.

[F2] J. Franks . Homology and Dynamical Systems. CBMS Regional Conf. Series in Math. 49. American Mathematical Society: Providence, RI, 1982.

[M1] J. Milnor . Lectures on the h-cobordism Theorem. Princeton Mathematical Notes. Princeton University Press: Princeton, 1965.

[M2] J. Milnor . A unique decomposition theorem for 3-manifolds. Amer. J. Math. 84 (1962), 17.

[S1] S. Smale . On gradient dynamical systems. Ann. Math. 74 (1961), 199206.

[S2] S. Smale . Generalized Poincaré's Conjecture in dimensions greater than four. Ann. Math. 74 (1961), 391406.

[Sm] J. Smoller . 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? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 1 *
Loading metrics...

Abstract views

Total abstract views: 53 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th May 2017. This data will be updated every 24 hours.