A Solvable N-body Problem of Goldfish Type Featuring N2 Arbitrary Coupling Constants

DOI10.1080/14029251.2016.1175823zbMath1421.70021OpenAlexW2317060910MaRDI QIDQ5231027

Francesco Calogero

Publication date: 29 August 2019

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

Full work available at URL: https://doi.org/10.1080/14029251.2016.1175823

zbMATH Keywords

integrable dynamical systemssolvable \(N\)-body problemsintegrable \(N\)-body problems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) (n)-body problems (70F10)

Related Items (8)

Zeros of entire functions and related systems of infinitely many nonlinearly coupled evolution equations ⋮ Yet another class of \textit{new solvable} \(N\)-body problems of goldfish type ⋮ Time-dependent polynomials with \textit {one double} root, and related new solvable systems of nonlinear evolution equations ⋮ Generations of monic polynomials such that the coefficients of each polynomial of the next generation coincide with the zeros of a polynomial of the current generation, and new solvable many-body problems ⋮ Generations of solvable discrete-time dynamical systems ⋮ A convenient expression of the time-derivative zn(k)(t) , of arbitrary order k, of the zero z _n (t) of a time-dependent polynomial p _N (z;t) of arbitrary degree N in z, and solvable dynamical systems ⋮ Novel solvable many-body problems ⋮ New solvable dynamical systems

Cites Work

• Unnamed Item
• Understanding complex dynamics by means of an associated Riemann surface
• The Lagrangian structure of Calogero's goldfish model
• Goldfish geodesics and Hamiltonian reduction of matrix dynamics
• The Painlevé property for quasihomogeneous systems and a many-body problem in the plane
• Solvable many-body models of goldfish type with one-, two- and three-body forces
• Eigenvalue-dynamics off the Calogero-Moser system
• Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve \(\mu^{2}= \nu^{n}-1, n \in \mathbb Z\): ergodicity, isochrony and fractals
• New Solvable Variants of the Goldfish Many-Body Problem
• Novel solvable extensions of the goldfish many-body model
• Novel solvable variants of the goldfish many-body model
• Goldfishing by gauge theory
• Calogero's  goldfish  is indeed a school of free particles
• Periodic Solutions of a Many-Rotator Problem in the Plane. II. Analysis of Various Motions
• A new solvable many-body problem of goldfish type
• Novel solvable many-body problems
• Time Discretization of F. Calogero's "Goldfish" System
• Isochronous Systems
• Towards a theory of chaos explained as travel on Riemann surfaces
• The transition from regular to irregular motions, explained as travel on Riemann surfaces
• The neatest many-body problem amenable to exact treatments (a ``goldfish?)

This page was built for publication: A Solvable N-body Problem of Goldfish Type Featuring N² Arbitrary Coupling Constants