On some applications of Sakai's geometric theory of discrete Painlevé equations

DOI10.3842/SIGMA.2018.075zbMath1396.37068arXiv1804.10341OpenAlexW2798809012MaRDI QIDQ1654171

Tomoyuki Takenawa, Anton Dzhamay

Publication date: 7 August 2018

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.10341

zbMATH Keywords

difference equationsintegrable systemPainlevé equationsbirational transformationisomonodromic transformation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Related Items (5)

Differential equations for the recurrence coefficients of semiclassical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach ⋮ A \(3 \times 3\) Lax form for the \(q\)-Painlevé equation of type \(E_6\) ⋮ Full-parameter discrete Painlevé systems from non-translational Cremona isometries ⋮ Gap probabilities in the Laguerre unitary ensemble and discrete Painlevé equations ⋮ Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations

Cites Work

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