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 Zap. Nauchn. Sem. POMI, 2018, Volume 468, Pages 221–227 (Mi znsl6582)

II

Links from second-order Fuchsian equations to first-order linear systems

M. V. Babichab, S. Yu. Slavyanova

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Abstract: The number of parameters in the linear Fuchsian system with four singularities is larger than that in the second-order Fuchsian equation with the same singularities. Hence, in order to find a relation between the given system and the equation it is needed to simplify the matrices – residues at finite Fuchsian singularities. The way to do it is studied. Such approach gives also the possibility to find the relation between the use of the antiquantization procedure and the isomonodromic property for derivation the Painlevé equation $P^{VI}$.

Key words and phrases: Heun equation, Fuchsian system, apparent singularity, isomonodromic deformation, Schlesinger system, antiquantization, Painlevé $P^{VI}$ equation.

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English version:
Journal of Mathematical Sciences (New York), 2019, 240:5, 646–650

UDC: 517.289+517.923+517.926

Citation: M. V. Babich, S. Yu. Slavyanov, “Links from second-order Fuchsian equations to first-order linear systems”, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Zap. Nauchn. Sem. POMI, 468, POMI, St. Petersburg, 2018, 221–227; J. Math. Sci. (N. Y.), 240:5 (2019), 646–650

Citation in format AMSBIB
\Bibitem{BabSla18} \by M.~V.~Babich, S.~Yu.~Slavyanov \paper Links from second-order Fuchsian equations to first-order linear systems \inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIX \serial Zap. Nauchn. Sem. POMI \yr 2018 \vol 468 \pages 221--227 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6582} \transl \jour J. Math. Sci. (N. Y.) \yr 2019 \vol 240 \issue 5 \pages 646--650 \crossref{https://doi.org/10.1007/s10958-019-04381-z} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85068151175}