On \(q\)-Painlevé VI and the geometry of Segre surfaces

(q)-calculus and related topics (05A30) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

Cites Work

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Algebraic solutions of the sixth Painlevé equation
Monodromy problem and the boundary condition for some Painlevé equations
Painlevé VI transcendents which are meromorphic at a fixed singularity.
Rational surfaces associated with affine root systems and geometry of the Painlevé equations
Carleson curves, Muckenhoupt weights, and Toeplitz operators
The general theory of linear \(q\)-difference equations.
The continuations of functions defined by generalised hypergeometric series.
Étude des différentes surfaces du quatrième ordre à conique double on cuspidale (générale ou décomposée) considérées comme des projections de l'intersection de deux variétés quadratiques de l'espace à quatre dimensions.
Monodromy of certain Painlevé-VI transcendents and reflection groups
Monodromy dependence and connection formulae for isomonodromic tau functions
Tau functions as Widom constants
A \(q\)-analog of the sixth Painlevé equation
Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions
On the Riemann-Hilbert problem for a \(q\)-difference Painlevé equation
Segre quartic surfaces and minitwistor spaces
A review of the sixth Painlevé equation
The non-singular cubic surfaces. A new method of investigation with special reference to questions of reality.
The space of monodromy data for the Jimbo-Sakai family of \(q\)-difference equations
Analytic solutions ofq-P(A₁) near its critical points
Geometric aspects of Painlevé equations
Lax Formalism for q-Painleve Equations with Affine Weyl Group Symmetry of Type EFormula
Del Pezzo surfaces of degree four
The logarithmic asymptotics of the sixth Painlevé equation
Asymptotic behaviour around a boundary point of theq-Painlevé VI equation and its connection problem
From Klein to Painlevé via Fourier, Laplace and Jimbo
CFT approach to the q-Painlevé VI equation
The Riemann–Hilbert Problem and Inverse Scattering
Tabulation of Painlevé 6 transcendents
Solving the Sixth Painlevé Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae
The Linear q-Difference Equation of the Second Order
On the monodromy manifold of \(q\)-Painlevé VI and its Riemann-Hilbert problem

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