Periods of the Goldfish Many-Body Problem

Sommacal, Matteo and Gomez-Ullate, D. (2005) Periods of the Goldfish Many-Body Problem. Journal of Non-linear Mathematical Physics, 12 (s1). pp. 351-362. ISSN 1402-9251

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Abstract

Calogero's goldfish N-body problem describes the motion of N point particles subject to mutual interaction with velocity-dependent forces under the action of a constant magnetic field transverse to the plane of motion. When all coupling constants are equal to one, the model has the property that for generic initial data, all motions of the system are periodic. In this paper we investigate which are the possible periods of the system for fixed N, and we show that there exist initial data that realize each of these possible periods. We then discuss the asymptotic behaviour of the maximal period for large particle number N.

Item Type:	Article
Subjects:	F300 Physics G100 Mathematics
Divisions:	Faculties > Engineering and Environment > School of Computing, Engineering and Information Sciences > Mathematics and Statistics
Related URLs:	Publisher
Depositing User:	Matteo Sommacal
Date Deposited:	09 May 2012 15:01
Last Modified:	22 Feb 2013 10:16
URI:	http://nrl.northumbria.ac.uk/id/eprint/6877