Variational formulas of the monodromy group for a third-order equation on a compact Riemann surface

Alexander V. Chueshev, Victor V. Chueshev

Kemerovo State University, Kemerovo, Russian Federation

Abstract: In the present article, we deduce explicit variational formulas for a solution vector and the elements of its monodromy group for a third-order ordinary differential equation on a compact Riemann surface of genus $g \geq 2$ in the spaces of quadratic and cubic holomorphic differentials.

Keywords: Riemann surface, third-order equation on a Riemann surface, variational formula, holomorphic differential.

UDC: 515:17+517:545

Received: 10.09.2021
Received in revised form: 10.11.2021
Accepted: 20.12.2021

Language: English

DOI: 10.17516/1997-1397-2022-15-3-308-318

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