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Semicontinuity of Majorants and Minorants of Lyapunov’s Exponents as Functions of Complex Parameter

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Abstract

A parametric family of linear differential systems with continuous coefficients bounded on the semi-axis and analytically dependent on a complex parameter is considered. It is established that the majorant (minorant) of the Lyapunov exponent considered as a function of the parameter is upper (lower) semicontinuous.

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References

  1. V. M. Millionshchikov, “Baire Classes of functions and Lyapunov Exponents,” Differ. Uravn. 16 (8), 1408 (1980).

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  2. A. N. Vetokhin, “On a Problem on Minorants of Lyapunov Exponents,” Differ. Uravn. 49 (7), 950 (2013) [Differ. Equations 49 (7), 922 (2013)].

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  3. V. M. Millionshchikov, “Majorants and Minorants of Extraordinary Lyapunov Exponents,” Differ. Uravn. 31 (9), 1601 (1995).

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  4. L. Hörmander, Introduction to Complex Analysis in Several Variables (Van Nostrand, 1967; Mir, Moscow, 1968).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow State University, Moscow, 119991, Russia

    A. N. Vetokhin

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  1. A. N. Vetokhin
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Correspondence to A. N. Vetokhin.

Additional information

Original Russian Text © A.N. Vetokhin. 2018. published in Vestnik Moskovskogo Universiteta. Matematika. Mekhanika. 2018. Vol. 73, No. 1, pp. 63-67.

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Vetokhin, A.N. Semicontinuity of Majorants and Minorants of Lyapunov’s Exponents as Functions of Complex Parameter. Moscow Univ. Math. Bull. 73, 34–37 (2018). https://doi.org/10.3103/S0027132218010060

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  • DOI: https://doi.org/10.3103/S0027132218010060

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