Journal of Nonlinear Mathematical Physics

Volume 20, Issue 1, April 2013, Pages 158 - 178

Diophantine Properties Associated to the Equilibrium Configurations of an Isochronous N-Body Problem

Authors
Oksana Bihun1, , Francesco Calogero2, , Ge Yi2,
Department of Mathematics, Concordia College at Moorhead, MN, USA
Physics Department, University of Rome “La Sapienza” and Istituto Nazionale di Fisica Nucleare, Sezione di Roma
Corresponding Authors
Oksana Bihun, Francesco Calogero, Ge Yi
Received 14 December 2012, Accepted 18 February 2013, Available Online 6 January 2021.
DOI
10.1080/14029251.2013.792494How to use a DOI?
Abstract

Recently a solvable N-body problem featuring several free parameters has been investigated, and conditions on these parameters have been identified which guarantee that this system is isochronous (all its solutions are periodic with a fixed period) and that it possesses equilibria. The N coordinates characterizing the equilibrium configurations are in some cases explicitly known, in others coincide with the N zeros of certain para-Jacobi polynomials or are arbitrary numbers. In the present paper the behavior of this N-body system in the immediate vicinity of its equilibria is studied, and Diophantine relations satisfied by the N coordinates are thereby identified.

Copyright
© 2013 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/).

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
20 - 1
Pages
158 - 178
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2013.792494How to use a DOI?
Copyright
© 2013 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/).

Cite this article

TY  - JOUR
AU  - Oksana Bihun
AU  - Francesco Calogero
AU  - Ge Yi
PY  - 2021
DA  - 2021/01/06
TI  - Diophantine Properties Associated to the Equilibrium Configurations of an Isochronous N-Body Problem
JO  - Journal of Nonlinear Mathematical Physics
SP  - 158
EP  - 178
VL  - 20
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2013.792494
DO  - 10.1080/14029251.2013.792494
ID  - Bihun2021
ER  -