Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
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Publication:1098980
DOI10.1007/BF01762370zbMath0637.34019MaRDI QIDQ1098980
Publication date: 1987
Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)
Related Items
Painlevé equations -- nonlinear special functions., Isomonodromy, Painlevé transcendents and scattering off of black holes, FROM KP/UC HIERARCHIES TO PAINLEVÉ EQUATIONS, A cubic Hamiltonian system with meromorphic solutions, Computation of \(RS\)-pullback transformations for algebraic Painlevé VI solutions, The five-vertex model and enumerations of plane partitions, Hamiltonians associated with the sixth Painlevé equation, Hypergeometric \(\tau\) functions of the \(q\)-Painlevé systems of types \(A_4^{(1)}\) and \((A_1+A_1')^{(1)}\), Singular instantons and Painlevé VI, Emptiness formation probability of the six-vertex model and the sixth Painlevé equation, Quantizing the discrete Painlevé VI equation: the Lax formalism, Basic asymptotic expansions of solutions to the sixth Painlevé equation, Classical conformal blocks and accessory parameters from isomonodromic deformations, Limit relation between Toda chains and the elliptic \(\mathrm{SL}(N,\mathbb{C})\) top, Toda equation and special polynomials associated with the Garnier system, Polynomial Hamiltonian systems with movable algebraic singularities, The sixth Painlevé equation as similarity reduction of \({\widehat{\mathfrak{gl}}_3}\) generalized Drinfel'd-Sokolov hierarchy, The diagonal two-point correlations of the Ising model on the anisotropic triangular lattice and Garnier systems, On transformations in the Painlevé family, Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation. I., Special function solutions of Painlevé equations: theory, asymptotics and applications, Riemann-Hilbert correspondence and blown up surface defects, Hiroshi Umemura and French mathematics, Special polynomials associated with the Painlevé equations. I, Notes on Umemura polynomials, The space of monodromy data for the Jimbo-Sakai family of \(q\)-difference equations, Circular pentagons and real solutions of Painlevé VI equations, Generalization of Okamoto's equation to arbitrary \(2\times 2\) Schlesinger system, Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces, Simply-laced isomonodromy systems, On the holonomic deformation of linear differential equations, From the Darboux-Egorov system to bi-flat \(F\)-manifolds, On Painlevé/gauge theory correspondence, Pole distribution of PVI transcendents close to a critical point, Reductions of Gauss-Codazzi Equations, Four-dimensional Painlevé-type equations associated with ramified linear equations. III: Garnier systems and Fuji-Suzuki systems, The sixth Painlevé transcendent and uniformization of algebraic curves, Form factor expansions in the 2D Ising model and Painlevé VI, Further results on non-diagonal: Bianchi type III vacuum metrics, The eight-vertex model and lattice supersymmetry, Spin chains with dynamical lattice supersymmetry, From hardcore bosons to free fermions with Painlevé V, Folding transformations of equations from the Gambier family, Geometric aspects of Painlevé equations, Reduction of lattice equations to the Painlevé equations: PIV and PV, An area-preserving action of the modular group on cubic surfaces and the Painlevé VI equation, On the Lax Pairs of the Symmetric Painlevé Equations, Symmetries of quantum Lax equations for the Painlevé equations, Non-integrability of some Painlevé VI-equations and dilogarithms, On the linearization of the Painlevé III–VI equations and reductions of the three-wave resonant system, 4-dimensional Frobenius manifolds and Painlevé VI, Algebro-geometric approach to an Okamoto transformation, the Painlevé VI and Schlesinger equations, Resolving singularities and monodromy reduction of Fuchsian connections, Schlesinger transformations for algebraic Painlevé VI solutions, The sixth Painlevé transcendents and the associated Schlesinger equation, Regge and Okamoto symmetries, Quantization of Calogero-Painlevé system and multi-particle quantum Painlevé equations II-VI, On reducible monodromy representations of some generalized Lamé equation, On determinant representation and integrability of Nekrasov functions, Geometric description of a discrete power function associated with the sixth Painlevé equation, Accessory parameters in conformal mapping: exploiting the isomonodromic tau function for Painlevé VI, Canonical structure and symmetries of the Schlesinger equations, Finite branch solutions to Painlevé VI around a fixed singular point, On algebraic relations between solutions of a generic Painlevé equation, On solutions of the Fuji-Suzuki-Tsuda system, Dynamics on character varieties and Malgrange irreducibility of Painlevé VI equation, Integral representation of solutions to Fuchsian system and Heun's equation, Paley-Wiener spaces with vanishing conditions and Painlevé VI transcendents, Bäcklund transformations for higher order Painlevé equations, Simple zero property of some holomorphic functions on the moduli space of tori, Classical transcendental solutions of the Painlevé equations and their degeneration, A \(\tau \)-function solution of the sixth Painlevé transcendent, Hamiltonian system for the elliptic form of Painlevé VI equation, The sigma form of the second Painlevé hierarchy, A class of differential equations of PI-type with the quasi-Painlevé property, Gravitational instantons with faster than quadratic curvature decay. III., On Gorenstein surfaces dominated by P2, Basic expansions of solutions to the sixth Painlevé equation in the generic case, The Lamé family of connections on the projective line, Conformal field theory of Painlevé VI, Transformations of spherical blocks, Deformations of the Zolotarev polynomials and Painlevé VI equations, Special polynomials related to the supersymmetric eight-vertex model: a summary, Asymptotic expansions of solutions of the sixth Painlevé equation, Nonperturbative theory of power spectrum in complex systems, Some explicit results for the generalized emptiness formation probability of the six-vertex model, Isomonodromic deformations and SU\(_2\)-invariant instantons on \(S^4\), Unnamed Item, Rational solutions of the classical Boussinesq system, Triangular Schlesinger systems and superelliptic curves, The fifty-two icosahedral solutions to Painlevé VI, Vector perturbations of Kerr-\(\mathrm{AdS}_5\) and the Painlevé VI transcendent, Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation, Bi-orthogonal systems on the unit circle, regular semi-classical weights and integrable systems. II, A simplified version of higher covariant derivative regularization, Painlevé equations and isomonodromic deformations of equations of the Heun class, Elliptic Calogero–Moser systems and isomonodromic deformations, Rational solutions of the Noumi and Yamada system of type $A_4^{(1)}$A4(1), Symmetries of the Garnier system and of the associated polynomial Hamiltonian system, A review of the sixth Painlevé equation, Regular non-semisimple Dubrovin–Frobenius manifolds, Global Asymptotics of the Sixth Painlevé Equation in Okamoto’s Space, Zeros of the isomonodromic tau functions in constructive conformal mapping of polycircular arc domains: the n-vertex case, QUANTUM PAINLEVÉ SYSTEMS OF TYPE $A_{n-1}^{(1)}$ WITH HIGHER DEGREE LAX OPERATORS, Generating functions related to the Okamoto polynomials for the Painlevé IV equation, The fourth Painlevé equation and associated special polynomials, Unnamed Item, A Truncation for Obtaining all the First Degree Birational Transformations of the Painlevé Transcendents, Hierarchies of Difference Equations and Bäcklund Transformations, Moyal Deformation of 2D Euler Equation and Discretization, Moduli spaces for the fifth Painlevé equation, Differential equations for the recurrence coefficients of semiclassical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach, Integrable differential systems for deformed Laguerre–Hahn orthogonal polynomials, Classification of algebraic solutions of irregular Garnier systems, The sixth Painlevé equation as isomonodromy deformation of an irregular system: monodromy data, coalescing eigenvalues, locally holomorphic transcendents and Frobenius manifolds, Holomorphic projective connections on surfaces, Nearest-neighbour correlation functions for the supersymmetric XYZ spin chain and Painlevé VI, Algebraic independence of generic Painlevé transcendents: PIII and PVI, Genus one Belyi maps by quadratic correspondences, Blowups in BPS/CFT correspondence, and Painlevé VI, Casorati determinant solutions for the discrete Painlevé III equation, Symmetric cubic surfaces and 𝐆₂ character varieties, New contiguity relation of the sixth Painlevé equation from a truncation, Grothendieck’s dessins d’enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations, Bäcklund transformations for certain rational solutions of Painlevé VI, The space of initial conditions and the property of an almost good reduction in discrete Painlevé II equations over finite fields, Note on algebro-geometric solutions to triangular Schlesinger systems, Proceedings of the 12th international workshop on nonlinear evolution equations and dynamical systems (NEEDS '98), Leeds, UK, June 21--28, 1998. Transl. from the Russian, Matrix Painlevé systems, RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION, Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation, Schwarz–Christoffel accessory parameter for quadrilaterals via isomonodromy, The Ising correlation C(M, N) for ν = −k, Resurgence, Painlevé equations and conformal blocks, Determinant formulas for the five-vertex model, Factorization of Ising correlations C(M, N) for ν = −k and M + N odd, M ⩽ N, T < T c and their lambda extensions, Discrete power functions on a hexagonal lattice I: derivation of defining equations from the symmetry of the Garnier system in two variables
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