Monodromy dependence and connection formulae for isomonodromic tau functions

DOI10.1215/00127094-2017-0055zbMath1396.33039arXiv1604.03082OpenAlexW2341782954MaRDI QIDQ1643998

Alexander R. Its, Andrei Prokhorov, Oleg Lisovyy

Publication date: 21 June 2018

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.03082

zbMATH Keywords

Teichmüller spacePoisson bracketVirasoro algebraCasimirsHamiltonian flowsLax pairPainlevé equationstau functiondigamma functionGoldman bracketGlaisher-Kinkelin constantFenchel-Nielsen coordinatesStokes phenomenonPoincaré indexSchlesinger systemsymplectic leafisomonodromyconnection problemBarnes \(G\)-functionskein relationansatzHastings-McLeod solutionRiemann-Hilbert methodAblowitz-Segur one-parameter family of solutionsBirkhoff-Grothendieck-Malgrange theorycanonical Darboux coordinatesconformal block representationsFlaschka-Newell Lax pairFricke coordinatesJimbo-Fricke cubic hypersurfaceJimbo-Miwa-Ueno tau functionMalgrange-Miwa theoremnonlinear special functionsnonresonant eigenvaluesRiemann-Hilbert mapRiemann-Hilbert representationStokes sectors

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Asymptotic expansions of solutions to ordinary differential equations (34E05) Painlevé-type functions (33E17) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

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