Completely integrable symplectic mapping

DOI10.3792/pjaa.63.198zbMath0634.58006OpenAlexW2082250296MaRDI QIDQ1096939

Shigeru Maeda

Publication date: 1987

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.63.198

zbMATH Keywords

complete integrabilityclassical mechanicscompletely integrable symplectic mapping

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (21)

Poisson brackets of mappings obtained as \((q,-p)\) reductions of lattice equations ⋮ Laurent phenomenon sequences ⋮ Bi-rational maps in four dimensions with two invariants ⋮ Quadratic conservatives of linear symplectic system ⋮ Discrete integrable systems and Poisson algebras from cluster maps ⋮ Coalgebra symmetry for discrete systems ⋮ Some integrable maps and their Hirota bilinear forms ⋮ Variational \(q\)-calculus. ⋮ Linear relations for Laurent polynomials and lattice equations ⋮ On reductions of the Hirota-Miwa equation ⋮ Variational calculus on \(q\)-nonuniform lattices ⋮ Integrable extensions of the Adler map via Grassmann algebras ⋮ Re-factorising a QRT map ⋮ Integrability of reductions of the discrete Korteweg–de Vries and potential Korteweg–de Vries equations ⋮ Invariants in separated variables: Yang-Baxter, entwining and transfer maps ⋮ LINEAR RELATIONS AND INTEGRABILITY FOR CLUSTER ALGEBRAS FROM AFFINE QUIVERS ⋮ Heron triangles with two rational medians and Somos-5 sequences ⋮ A Novel Integrable Fourth-Order Difference Equation Admitting Three Invariants ⋮ Integrable symplectic maps ⋮ Entwining Yang–Baxter maps related to NLS type equations ⋮ 2ⁿ-rational maps

Cites Work

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• First integrals in the discrete variational calculus
• Recent Developments in the Theory of Hamiltonian Systems
• Generic Hamiltonian dynamical systems are neither integrable nor ergodic

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