Integrable Hamiltonian N-body problems of goldfish type featuring N arbitrary functions

DOI

10.1080/14029251.2016.1274110How to use a DOI?

Keywords

integrable many-body Hamiltonian systems in the plane; integrable many-body systems with Newtonian (accelerations equal forces) equations of motion

Abstract

A simple application of a neat formula relating the time evolution of the N zeros of a (monic) time-dependent polynomial of degree N in the complex variable w to the time evolution of its N coefficients allows to identify integrable Hamiltonian N-body problems in the plane featuring N arbitrary functions, the equations of motions of which are of Newtonian type: accelerations equal forces nonlinearly dependent on the coordinates of the N particle. The motions generally take place in the complex z-plane, or, equivalently, in the Cartesian xy-plane with z = x + iy. It is also easy to identify qualitative features of special subclasses of these models, for instance cases in which all the motions starting from an arbitrary real set of initial data are confined and multiply periodic. It is also indicated how to generate from these models hierarchies of analogous models with analogous properties.

Copyright

© 2017 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Francesco Calogero
PY  - 2021
DA  - 2021/01/06
TI  - Integrable Hamiltonian N-body problems of goldfish type featuring N arbitrary functions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 6
VL  - 24
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1274110
DO  - 10.1080/14029251.2016.1274110
ID  - Calogero2021
ER  -