Skip to main content
Log in

Conditions for Instability of an Invariant Toroidal Manifold of a Discrete Dynamical System in a Banach Space

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain conditions for the instability of an invariant toroidal manifold of a discrete dynamic system.

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.

Similar content being viewed by others

REFERENCES

  1. M. W. Hirsch, Differential Topology, Springer, New York (1966).

    Google Scholar 

  2. D. V. Anosov, S. Kh. Aranson, I. U. Bronshtein, and V. Z. Grines, “Smooth dynamical systems,” in: VINITI Series in Contemporary Problems in Mathematics. Fundamental Trends [in Russian], Vol. 1, VINITI, Moscow (1985), pp. 151–242.

    Google Scholar 

  3. A. M. Samoilenko and V. V. Slyusarchuk, “Discrete dynamical systems with invariant asymptotically stable toroidal manifold,” Ukr. Mat. Zh., 51, No. 4, 466–471 (1999).

    Google Scholar 

  4. J. W. Milnor and A. H. Wallace, Differential Topology. First Course [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  5. S. G. Krein, Linear Equations in Banach Spaces [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  6. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin (1966).

    Google Scholar 

  7. A. G. Kurosh, A Course in Higher Algebra [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  8. A. M. Samoilenko, V. E. Slyusarchuk, and V. V. Slyusarchuk, “Investigation of a nonlinear difference equation in a Banach space in the neighborhood of a quasiperiodic solution,” Ukr. Mat. Zh., 49, No. 12, 1661–1676 (1997).

    Google Scholar 

  9. A. M. Samoilenko, “Investigation of a discrete dynamical system in the neighborhood of a quasiperiodic trajectory,” Ukr. Mat. Zh., 44, No. 12, 1702–1711 (1992).

    Google Scholar 

  10. A. M. Samoilenko, V. E. Slyusarchuk, and V. V. Slyusarchuk, “On one operator equation in the theory of discrete dynamical systems,” Nelin. Kolyv., 2, No. 2, 241–251 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Slyusarchuk, V.V. Conditions for Instability of an Invariant Toroidal Manifold of a Discrete Dynamical System in a Banach Space. Ukrainian Mathematical Journal 53, 656–662 (2001). https://doi.org/10.1023/A:1012343108603

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012343108603

Keywords

Navigation