On Simplified Formulas for the Central Exponents of Differential Systems With Non-Uniform Scales

On Simplified Formulas for the Central Exponents of Differential Systems With Non-Uniform Scales

We study the Vinograd–Millionshchikov central exponents, which represent the exact outer boundaries for the mobility of the extremal values of the Lyapunov and Perron exponents of a linear differential system under uniformly small perturbations of its coefficients. We prove the possibility of calcul...

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Bibliographic Details
Published in:Russian mathematics Vol. 62; no. 10; pp. 51 - 67
Main Author: Sergeev, I. N.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01-10-2018
Springer Nature B.V
Subjects:
Exponents
Mathematical analysis
Mathematics
Mathematics and Statistics
differential equation
linear system
Lyapunov exponents
central exponents
stability
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Summary:We study the Vinograd–Millionshchikov central exponents, which represent the exact outer boundaries for the mobility of the extremal values of the Lyapunov and Perron exponents of a linear differential system under uniformly small perturbations of its coefficients. We prove the possibility of calculating those exponents using simplified formulas with expanding time scales and obtain concrete estimates for the central exponents with simplified ones, calculated in different scales: thick, expanding, slowly expanding and sparse.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X18100079