Skip to main content
Log in

Topological classification of Morse-Smale diffeomorphisms with finite set of heteroclinic trajectories on surfaces

  • Published:
Mathematical Notes Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. S. Smale, “Differentiable dynamical systems,” Bull. Amer. Math. Soc.,73, No. 6, 113–185 (1967).

    Google Scholar 

  2. A. N. Bezdenezhnykh and V. Z. Grines, “Realization of gradient-like diffeomorphisms of two-dimensional manifolds,” in: N. F. Otrokov (ed.), Differential and Integral Equations [in Russian], Gor'kii Gos. Univ., Gor'kii (1985), pp. 33–37.

    Google Scholar 

  3. A. N. Bezdenezhnykh and V. Z. Grines, “Diffeomorphisms with orientable heteroclinic sets on two-dimensional manifolds,” in: E. A. Leontovich-Andronovoi (ed.), Methods of the Qualitative Theory of Differential Equations [in Russian], Gor'kii (1985), pp. 139–152.

  4. A. N. Bezdenezhnykh and V. Z. Grines, “Dynamic properties and topological classification of gradient-like diffeomorphisms on two-dimensional manifolds, Part 1, in: E. A. Leontovich-Andronovoi (ed.), Methods of the Qualitative Theory of Differential Equations [in Russian], Gor'kii (1985), pp. 139–152; Part 2, ibid., (1987), pp. 24–32.

  5. E. A. Borevich, “Conditions for topological equivalence of two-dimensional Morse-Smale diffeomorphisms,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 12–17 (1980).

    Google Scholar 

  6. E. A. Borevich, “Conditions for topological equivalence of two-dimensional Morse-Smale diffeomorphisms,” Differents. Uravn.,17, No. 8, 1481–1482 (1981).

    Google Scholar 

  7. E. A. Borevich, “Topological equivalence of two-dimensional Morse-Smale diffeomorphisms,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 3–6 (1984).

    Google Scholar 

  8. E. A. Borevich, “Two-dimensional Morse-Smale systems having oriented heteroclinic relations,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 77–79 (1989).

    Google Scholar 

  9. Ya. L. Umanskii, “Necessary and sufficient conditions for the topological equivalence of three-dimensional Morse-Smale dynamical systems with a finite number of singular trajectories,” Mat. Sborn.,181, No. 2, 212–239 (1990).

    Google Scholar 

  10. J. Palis, “On Morse-Smale dynamical systems,” Topology,8, No. 4, 385–404 (1969).

    Google Scholar 

  11. M. Peixoto, “On the classification of flows on two-manifolds,” in: M. Peixoto (ed.), Dynamical Systems. Proc. Symp. held at the Univ. of Bahia, Salvador, Brasil, 1971, Academic Press, New York-London (1973), pp. 389–419.

    Google Scholar 

  12. J. Palis and S. Smale, “Structural stability theorems,” [Russian translation], Matematika,13, No. 2, 145–155 (1969).

    Google Scholar 

  13. V. S. Medvedev, “Behavior of trajectories of a cascade in a neighborhood of an invariant set,” Differents. Uravn.,13, 1192–1201 (1977).

    Google Scholar 

  14. S. Kh. Aranson and V. Z. Grines, “Cascades on surfaces,” in: Dynamical Systems 9. Itogi Nauki i Tekhniki. Sovremennye Problemy Matematiki. Fundamental'nye Napravleniya,66, 148–187 (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 54, No. 3, pp. 3–17, September, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grines, V.Z. Topological classification of Morse-Smale diffeomorphisms with finite set of heteroclinic trajectories on surfaces. Math Notes 54, 881–889 (1993). https://doi.org/10.1007/BF01209552

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01209552

Keywords

Navigation