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A criterion for the stability of Lyapunov exponents with respect to perturbations, small in the mean, in the class of regular systems

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Abstract

Expressions for the exact bounds of mobility of the Lyapunov exponents are obtained in terms of the Cauchy operator of a linear system of differential equations in the set of regular systems, endowed with the mean convergence topology.

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Literature Cited

  1. I. N. Sergeev, "Lyapunov exponents of regular systems with perturbations that are small in the mean," Trudy Sem. Petrovsk. No. 13, 166–176 (1988).

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  2. B. F. Bylov, R. E. Vinograd, D. M. Grobman, and V. V. Nemytskii, The Theory of Lyapunov Exponents and Its Applications to Problems of Stability [in Russian], Nauka, Moscow (1966).

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  3. I. N. Sergeev, "On the destabilizability of regular systems," Usp. Mat. Nauk,44, No. 4, 209–210 (1989).

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Authors
  1. I. N. Sergeev
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Additional information

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 16, pp. 236–241, 1992.

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Sergeev, I.N. A criterion for the stability of Lyapunov exponents with respect to perturbations, small in the mean, in the class of regular systems. J Math Sci 69, 1105–1109 (1994). https://doi.org/10.1007/BF01254396

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  • DOI: https://doi.org/10.1007/BF01254396

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