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The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients

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Abstract

By the direct Lyapunov method we prove a sufficient condition for the exponential dichotomy with a weakened (in comparison with the case of arbitrary coefficients) requirement to the difference derivative of the Lyapunov function along the system trajectory. We give an illustrative example.

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Authors and Affiliations

  1. Omsk State Technical University, pr. Mira 11, Omsk, 644050, Russia

    R. K. Romanovskii & L. V. Bel’gart

Authors
  1. R. K. Romanovskii
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  2. L. V. Bel’gart
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Correspondence to L. V. Bel’gart.

Additional information

Original Russian Text © R.K. Romanovskii and L.V. Bel’gart, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 10, pp. 51–59.

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Romanovskii, R.K., Bel’gart, L.V. The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients. Russ Math. 54, 44–51 (2010). https://doi.org/10.3103/S1066369X10100051

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  • DOI: https://doi.org/10.3103/S1066369X10100051

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