The dependence on the monodromy data of the isomonodromic tau function

DOI10.1007/s00220-009-0961-7zbMath1218.37099arXiv0902.4716OpenAlexW3099699439MaRDI QIDQ625466

Marco Bertola

Publication date: 17 February 2011

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.4716

zbMATH Keywords

Riemann-Hilbert problemdeformationPainlevé II equationmonodromy mapisomonodromic tau functionMalgrange divisor

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

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Cites Work

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• Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III
• Complex path integral representation for semiclassical linear functionals
• Bilinear semiclassical moment functionals and their integral representation
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• On semiclassical linear functionals: Integral representations
• Biorthogonal Laurent polynomials, toplitz determinants, minimal Toda orbits and isomonodromic tau functions
• Zeros of the Jimbo, Miwa, Ueno tau function
• Moment determinants as isomonodromic tau functions
• Symplectic manifolds and isomonodromic deformations