Ukrainian Mathematical Journal

, Volume 50, Issue 3, pp 514–516 | Cite as

Conditions for exponential stability and dichotomy of pulse linear extensions of dynamical systems on a torus

  • S. V. Yanchuk
  • N. A. Ali
Brief Communications

Abstract

Conditions for exponential stability and dichotomy of pulse linear extensions of dynamical systems on a torus are investigated.

Keywords

Limit Point Exponential Stability Lipschitz Condition Invariant Tori Ukrainian Academy 

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References

  1. 1.
    A. M. Samoilenko, “On some problems of the theory of perturbations for smooth invariant tori of dynamical systems,” Ukr. Mat. Zh., 46, No. 12, 1665–1700 (1994).CrossRefGoogle Scholar
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    V. I. Tkachenko, “The Green function and conditions of the existence of invariant sets of pulse systems,” Ukr. Mat. Zh., 41, No. 10, 1379–1383 (1989).CrossRefMathSciNetGoogle Scholar
  3. 3.
    A. M. Samoilenko and N. I. Perestyuk, Differential Equations with Pulse Action [in Russian], Vyshcha Shkola, Kiev (1987).Google Scholar
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    A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • S. V. Yanchuk
    • 1
  • N. A. Ali
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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