Construction of the Fuchs equation with four given finite critical points and a given reducible monodromy group in the resonance case
https://doi.org/10.29235/1561-2430-2019-55-2-199-206
Abstract
One inverse problem of the analytic theory of linear differential equations is considered. Namely, the completely integrable Fuchs equation with four given finite critical points and a given reducible monodromy group of rank 2 on the complex projective line is constructed. Reducibility of the monodromy group of rank 2 means that 2×2-monodromy matrices (the generators of the monodromy group) can be simultaneously reduced by a linear nonsingular transformation to an upper triangular form. In so doing we study the case when the eigenvalue ξj of the diagonal matrix of the monodromy formal exponent at a corresponding Fuchs critical point is equal to an integer different from zero (resonance takes place).
About the Authors
V. V. Amel’kin
Belarusian State University
Belarus
Belarus
Vladimir V. Amel’kin – Dr. Sc. (Physics and Mathematics), Professor, Professor of the Department of Differential Equations and Systemic Analysis
4, Nezavisimosti Ave, 220030, Minsk, Republic of Belarus
M. N. Vasilevich
Belarusian State University
Belarus
Belarus
Michail N. Vasilevich – Ph. D. (Physics and Mathematics), Assistant professor of the Department of General Mathematics and Informatics
4, Nezavisimosti Ave, 220030, Minsk, Republic of Belarus
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