On the autonomous limit of discrete Painlevé equations

DOI10.1016/S0378-4371(01)00619-7zbMath0992.39015MaRDI QIDQ5959005

Alfred Ramani, Yasuhiro Ohta, A. S. Carstea, Basile Grammaticos

Publication date: 20 March 2002

Published in: Physica A (Search for Journal in Brave)

zbMATH Keywords

autonomous systemsdiscrete Painlevé equationsQRT mapping

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12)

Related Items (25)

Solving the Quispel–Roberts–Thompson maps using Kajiwara–Noumi–Yamada’s representation of elliptic curves ⋮ On the integrability of correspondences associated to integral curves ⋮ Integrable mappings with transcendental invariants ⋮ From integrable lattices to non-QRT mappings ⋮ Investigating relations between discrete Painlevé equations: The multistep approach ⋮ Integrable non-QRT mappings of the plane ⋮ On a novel representation of discrete Painlevé equations ⋮ Coalgebra symmetry for discrete systems ⋮ Existence of meromorphic solutions of first-order difference equations ⋮ A systematic method for constructing discrete Painlevé equations in the degeneration cascade of the E8 group ⋮ On meromorphic solutions of Malmquist type difference equations ⋮ Rational solutions of difference Painlevé equations ⋮ Hankel determinant solution for elliptic sequence ⋮ A class of integrable and nonintegrable mappings and their dynamics ⋮ Strongly asymmetric discrete Painlevé equations: The additive case ⋮ Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings ⋮ Strongly asymmetric discrete Painlevé equations: The multiplicative case ⋮ Constructing discrete Painlevé equations: from E8(1) to A1(1) and back ⋮ Restoring discrete Painlevé equations from an E8(1)-associated one ⋮ A new family of discrete Painlevé equations and associated linearisable systems ⋮ Interrelations of discrete Painlevé equations through limiting procedures ⋮ On the canonical forms of QRT mappings and discrete Painlevé equations ⋮ Discretising the Painlevé equations à la Hirota-Mickens ⋮ On Quispel-Roberts-Thompson extensions and integrable correspondences ⋮ A class of integrable non-QRT mappings and their deautonomisation

Cites Work

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• Growth and integrability in the dynamics of mappings
• From continuous to discrete Painlevé equations
• Retracing the Painlevé-Gambier classification for discrete systems
• The hunting for the discrete Painlevé equations
• Integrable mappings and soliton equations. II
• Discrete Painlevé equations: coalescences, limits and degeneracies
• Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations
• Integrable mappings of the plane preserving biquadratic invariant curves
• Discrete versions of the Painlevé equations
• Do integrable mappings have the Painlevé property?
• On a class of special solutions of the Painlevé equations

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