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Functions Determined by the Lyapunov Exponents of Families of Linear Differential Systems Continuously Depending on the Parameter Uniformly on the Half-Line

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Abstract

For families of n-dimensional linear differential systems (n ≥ 2) whose dependence on a parameter ranging in a metric space is continuous in the sense of the uniform topology on the half-line, we obtain a complete description of the ith Lyapunov exponent as a function of the parameter for each i = 1,..., n. As a corollary, we give a complete description of the Lebesgue sets and (in the case of a complete separable parameter space) the range of an individual Lyapunov exponent of such a family.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    V. V. Bykov

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  1. V. V. Bykov
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Correspondence to V. V. Bykov.

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Original Russian Text © V.V. Bykov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 12, pp. 1579–1592.

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Bykov, V.V. Functions Determined by the Lyapunov Exponents of Families of Linear Differential Systems Continuously Depending on the Parameter Uniformly on the Half-Line. Diff Equat 53, 1529–1542 (2017). https://doi.org/10.1134/S0012266117120011

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  • DOI: https://doi.org/10.1134/S0012266117120011

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