The number of discrete Painlevé equations is infinite

DOI10.1016/j.physleta.2009.06.034zbMath1233.34038OpenAlexW2022584943MaRDI QIDQ665272

Alfred Ramani, Basile Grammaticos

Publication date: 5 March 2012

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2009.06.034

zbMATH Keywords

Weyl groupsintegrable mappingsdiscrete Painlevé equations

Mathematics Subject Classification ID

Weyl theory and its generalizations for ordinary differential equations (34B20) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series (11F68)

Related Items (7)

On a novel representation of discrete Painlevé equations ⋮ Geometric aspects of Painlevé equations ⋮ On the limits of discrete Painlevé equations associated with the affine Weyl group E8 ⋮ Miura transformations for discrete Painlevé equations coming from the affine E8 Weyl group ⋮ Full-parameter discrete Painlevé systems from non-translational Cremona isometries ⋮ Strongly asymmetric discrete Painlevé equations: The additive case ⋮ Restoring discrete Painlevé equations from an E8(1)-associated one

Cites Work

• Self-duality and Schlesinger chains for the asymmetric \(\text{d-P}_{\text{II}}\) and \(\text{q-P}_{\text{III}}\) equations
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Discrete Painlevé equations: coalescences, limits and degeneracies
• Generating discrete Painlevé equations from affine Weyl groups
• From continuous Painlevé IV to the asymmetric discrete Painlevé I
• Elliptic discrete Painlev  equations
• Discrete versions of the Painlevé equations
• A study on the fourthq-Painlevé equation
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