A new class of solvable dynamical systems

DOI10.1063/1.2920569zbMath1152.81359OpenAlexW1974103160MaRDI QIDQ5504907

Francesco Calogero

Publication date: 23 January 2009

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

Full work available at URL: https://doi.org/10.1063/1.2920569

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Dynamics induced by flows and semiflows (37C10) Periodic orbits of vector fields and flows (37C27) (n)-body problems (70F10) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06)

Related Items (3)

Dynamical and spectral Dirac systems: response function and inverse problems ⋮ Solvable Systems of Isochronous, Multi-Periodic or Asymptotically Isochronous Nonlinear Oscillators ⋮ Isochronous Dynamical System and Diophantine Relations I

Cites Work

• On the integrability of certain matrix evolution equations
• A generalisation of the Calogero-Moser system
• Three integrable Hamiltonian systems connected with isospectral deformations
• Eigenvalue-dynamics off the Calogero-Moser system
• A technique to identify solvable dynamical systems, and another solvable extension of the goldfish many-body problem
• New solvable many-body problems in the plane
• Novel solvable extensions of the goldfish many-body model
• Novel solvable variants of the goldfish many-body model
• Isochronous and partially isochronous Hamiltonian systems are not rare
• Goldfishing by gauge theory
• Two novel classes of solvable many-body problems of goldfish type with constraints
• A new class of solvable many-body problems with constraints, associated with an exceptional polynomial subspace of codimension 2
• Hamiltonian group actions and dynamical systems of calogero type
• Nonlinear harmonic oscillators
• A technique to identify solvable dynamical systems, and a solvable generalization of the goldfish many-body problem
• Erratum: Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials [J. Math. Phys. 12, 419–436 (1971)]
• Isochronous Systems

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