Volume 16, Issue 1, March 2009, Pages 105 - 116
Isochronous Dynamical System and Diophantine Relations I
F. Calogero*, †, ‡, S. Iona*, §
*Dipartimento di Fisica, Università di Roma, “La Sapienza”, Rome, Italy
†Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy
Received 8 April 2008, Accepted 28 May 2008, Available Online 7 January 2021.
- 10.1142/S1402925109000091How to use a DOI?
- Dynamical systems; integrable; isochronous; Diophantine; matrices; eigenvalues; conjectures; nonlinear harmonic oscillators
We identify a solvable dynamical system — interpretable to some extent as a many-body problem — and point out that — for an appropriate assignment of its parameters — it is entirely isochronous, namely all its nonsingular solutions are completely periodic (i.e., periodic in all degrees of freedom) with the same fixed period (independent of the initial data). We then identify its equilibrium configurations and investigate its behavior in their neighborhood. We thereby identify certain matrices — of arbitrary order — whose eigenvalues are all rational numbers: a Diophantine finding.
- © 2009 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 - F. Calogero AU - S. Iona PY - 2021 DA - 2021/01/07 TI - Isochronous Dynamical System and Diophantine Relations I JO - Journal of Nonlinear Mathematical Physics SP - 105 EP - 116 VL - 16 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925109000091 DO - 10.1142/S1402925109000091 ID - Calogero2021 ER -