Variational formulas of~the~monodromy group for~a~third-order equation on~a~compact Riemann surface
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 3, pp. 308-318.

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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, holomorphic differential.
Mots-clés : variational formula
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Alexander V. Chueshev; Victor V. Chueshev. Variational formulas of~the~monodromy group for~a~third-order equation on~a~compact Riemann surface. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 3, pp. 308-318. http://geodesic.mathdoc.fr/item/JSFU_2022_15_3_a4/

[1] D.A. Hejhal, “Monodromy groups for higher-order differentials equation”, Bull. Amer. Math. Soc., 81:3 (1975), 590–592 | DOI | MR | Zbl

[2] D.A. Hejhal, “Monodromy groups and linearly polymorphic functions”, Acta Math., 135:1-2 (1975), 1–55 | DOI | MR | Zbl

[3] D.A. Hejhal, “The variational theory of linearly polymorphic functions”, J. d'Analyse Math., 30 (1976), 215–264 | DOI | MR | Zbl

[4] V.V. Chueshev, “An Explicit Variational Formula for the Monodromy Group”, Siberian Adv. Math., 15:22 (2005), 1–32 (in Russian) ; Mat. Tr., 7:2 (2004), 126–158 | MR | Zbl | MR

[5] H.M. Farkas, I. Kra, Riemann surfaces, Grad. Text's Math., 71, Springer, New-York, 1992 | DOI | MR | Zbl

[6] M.I. Tulina, “Explicit variational formulas for third-order equations on Riemann surfaces”, Journal of Siberian Federal University. Mathematics $\$ Physics, 6:3 (2013), 365–375 | Zbl

[7] A.V. Chueshev, V.V. Chueshev, “The residue theorem and an analog of P. Appell's formula for finite Riemann surface”, Science Evolution, 1:1 (2016), 40–45 | DOI | MR