Connection Coefficients and Monodromy Representations for a Class of Okubo Systems of Ordinary Differential Equations

Konnai, Shotaro

doi:10.1619/fesi.61.145

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2021

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“…have been studied extensively in the literature [1][2][3][4][5][6][7][8][9][10][11][12]. In [1], the authors study system [13] under the assumption that A 0 has all distinct eigenvalues and introduce one scalar function that allows representing all solutions of the system.…”

Section: Introductionmentioning

confidence: 99%

On the Solutions of Okubo-Type Systems

Filipuk

Lastra

2021

Journal of Mathematics

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We show that for certain systems of Okubo-type, we can find a solution vector, all components of which are expressed in terms of the first one. This first component can be expressed in two ways. It solves a Volterra integral equation with the kernel expressed in terms of the solutions of a reduced Okubo-type system of smaller dimension. It is also expressed as a power series about the origin with coefficients satisfying certain recurrence relation. This extends the results in (W. Balser, C. Röscheisen, J. Differential Equations, 2009).

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