Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations

DOI10.1016/S0375-9601(99)00670-2zbMath0939.37041arXivsolv-int/9910007MaRDI QIDQ1967014

K. M. Tamizhmani, Yasuhiro Ohta, Basile Grammaticos, Alfred Ramani

Publication date: 8 March 2000

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

Full work available at URL: https://arxiv.org/abs/solv-int/9910007

zbMATH Keywords

Painlevé equationssingularity confinementintegrability criterionnonautonomous mapping

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25)

Related Items (17)

Exact localized solutions of quintic discrete nonlinear Schrödinger equation ⋮ Growth of degrees of integrable mappings ⋮ Integrable mappings with transcendental invariants ⋮ Periodicity and integrability for the cube recurrence ⋮ A note on globally periodic maps and integrability ⋮ On the limits of discrete Painlevé equations associated with the affine Weyl group E8 ⋮ \(R\)-systems ⋮ Do all integrable equations satisfy integrability criteria? ⋮ On the autonomous limit of discrete Painlevé equations ⋮ From discrete integrable equations to Laurent recurrences ⋮ The road to the discrete analogue of the Painlevé property: Nevanlinna meets singularity confinement ⋮ Hirota's method and the search for integrable partial difference equations. 1. Equations on a 3 × 3 stencil ⋮ Calculation of algebraic entropies of d-PIV and d-PV ⋮ Integrable lattice equations and their growth properties ⋮ Dynamics of Nonpolar Solutions to the Discrete Painlevé I Equation ⋮ Calculating algebraic entropies: an express method ⋮ What is the discrete analogue of the Painlevé property?

Cites Work

• Growth and integrability in the dynamics of mappings
• Nonlinear nonautonomous discrete dynamical systems from a general discrete isomonodromy problem
• From continuous to discrete Painlevé equations
• Algebraic entropy
• Integrable mappings and soliton equations. II
• A \(q\)-analog of the sixth Painlevé equation
• On a novel \(q\)-discrete analogue of the Painlevé VI equation
• Dynamics of complexity of intersections
• From continuous Painlevé IV to the asymmetric discrete Painlevé I
• Degeneration through coalescence of theq-Painlevé VI equation
• Discrete versions of the Painlevé equations
• Do integrable mappings have the Painlevé property?
• Linearization and solutions of the discrete Painlevé III equation
• Discrete dressing transformations and Painlevé equations

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