Jacobi's last multiplier, Lie symmetries, and hidden linearity: ``goldfishes galore

DOI10.1007/s11232-007-0070-8zbMath1137.70010OpenAlexW2034984602MaRDI QIDQ926758

Maria Clara Nucci

Publication date: 20 May 2008

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-007-0070-8

zbMATH Keywords

Einstein-Yang-Mills equationsCalogero's many-body problem

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

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Uses Software

• REDUCE

Cites Work

• Let's Lie: A miraculous haul of fishes
• Hidden linearity in systems for competition with evolution in ecology and finance
• The Painlevé property for quasihomogeneous systems and a many-body problem in the plane
• The harmony in the Kepler and related problems
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• Calogero's  goldfish  is indeed a school of free particles
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• Lie point symmetries and first integrals: The Kowalevski top
• Lorenz integrable system moves à la Poinsot
• Reduction of the classical MICZ-Kepler problem to a two-dimensional linear isotropic harmonic oscillator
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• Jacobi Last Multiplier and Lie Symmetries: A Novel Application of an Old Relationship
• Formal and analytic first integrals of the Einstein–Yang–Mills equations
• The neatest many-body problem amenable to exact treatments (a ``goldfish?)
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