The Painlevé property for quasihomogeneous systems and a many-body problem in the plane
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Publication:1781835
DOI10.1007/s00220-004-1284-3zbMath1069.81079OpenAlexW1998463976MaRDI QIDQ1781835
Publication date: 8 June 2005
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00220-004-1284-3
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) (n)-body problems (70F10)
Related Items (7)
Yet another class of \textit{new solvable} \(N\)-body problems of goldfish type ⋮ Semicompleteness of homogeneous quadratic vector fields ⋮ Jacobi's last multiplier, Lie symmetries, and hidden linearity: ``goldfishes galore ⋮ Solution of the Goldfish N-Body Problem in the Plane with (Only) Nearest-Neighbor Coupling Constants All Equal to Minus One Half ⋮ Quantizing preserving Noether symmetries ⋮ A Solvable N-body Problem of Goldfish Type Featuring N2 Arbitrary Coupling Constants ⋮ New solvable dynamical systems
Cites Work
- Periodic solutions of a many-rotator problem in the plane
- On a new integrable Hamiltonian system with nearest-neighbour interaction
- Solution of the Goldfish N-Body Problem in the Plane with (Only) Nearest-Neighbor Coupling Constants All Equal to Minus One Half
- General solution of a three-body problem in the plane
- Periodic Solutions of a Many-Rotator Problem in the Plane. II. Analysis of Various Motions
- A further solvable three-body problem in the plane
- A global formulation of the Lie theory of transformation groups
- Necessary condition for the existence of algebraic first integrals
- The neatest many-body problem amenable to exact treatments (a ``goldfish?)
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