Goldfish geodesics and Hamiltonian reduction of matrix dynamics

DOI10.1007/s11005-008-0232-0zbMath1153.37398arXivmath-ph/0702091OpenAlexW3100795316MaRDI QIDQ934991

Joakim Arnlind, Jens Hoppe, Martin Bordemann, Choonkyu Lee

Publication date: 31 July 2008

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

Full work available at URL: https://arxiv.org/abs/math-ph/0702091

zbMATH Keywords

Integrable systemsGoldfish modelRuijsennaars-Schneider system

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (10)

Ruijsenaars-Schneider three-body models with \(N=2\) supersymmetry ⋮ Yet another class of \textit{new solvable} \(N\)-body problems of goldfish type ⋮ Novel isochronous N-body problems featuring N arbitrary rational coupling constants ⋮ Geodesic compatibility: goldfish systems ⋮ Integrability of \(\mathcal{N} = 1\) supersymmetric Ruijsenaars-Schneider three-body system ⋮ Supersymmetric many-body Euler-Calogero-Moser model ⋮ \(\mathcal{N}\)-extended supersymmetric Calogero models ⋮ A Solvable N-body Problem of Goldfish Type Featuring N² Arbitrary Coupling Constants ⋮ New solvable dynamical systems ⋮ \( \mathcal{N} =2 \) supersymmetric extensions of relativistic Toda lattice

Cites Work

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• Hamiltonian character of the motion of the zeros of a polynomial whose coefficients oscillate over time
• Introduction to Classical Integrable Systems
• A technique to identify solvable dynamical systems, and a solvable generalization of the goldfish many-body problem
• The neatest many-body problem amenable to exact treatments (a ``goldfish?)

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