Singularity confinement and algebraic integrability

DOI10.1063/1.1640797zbMath1070.37039arXivnlin/0311014OpenAlexW1988724775MaRDI QIDQ4833355

Stéphane Lafortune, Alain Goriely

Publication date: 15 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0311014

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Discrete version of topics in analysis (39A12)

Related Items (10)

Riemann-Hilbert Problems, Matrix Orthogonal Polynomials and Discrete Matrix Equations with Singularity Confinement ⋮ Integrable mappings of the plane preserving biquadratic invariant curves. III ⋮ Real dynamics of integrable birational maps ⋮ A note on globally periodic maps and integrability ⋮ Direct method to construct integrals for N th-order autonomous ordinary difference equations ⋮ Painlevé Tests, Singularity Structure and Integrability ⋮ Derivation of invariant varieties of periodic points from singularity confinement in the case of Toda map ⋮ Polynomial integrals for third- and fourth-order ordinary difference equations ⋮ Global periodicity and complete integrability of discrete dynamical systems ⋮ Dynamics of Nonpolar Solutions to the Discrete Painlevé I Equation

Cites Work

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• The Gambier mapping, revisited
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• Algebraic entropy
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• The Gambier mapping
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• Algebraic entropy of birational maps with invariant curves
• Integrable mappings of the plane preserving biquadratic invariant curves
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• Integrable maps
• A new class of integrable discrete systems
• Discrete versions of the Painlevé equations
• Do integrable mappings have the Painlevé property?
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• Integrable mappings of the plane preserving biquadratic invariant curves II
• Superintegrability with third-order integrals in quantum and classical mechanics
• Non-proliferation of pre-images in integrable mappings
• Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations
• Necessary condition for the existence of algebraic first integrals
• Necessary condition for the existence of algebraic first integrals

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