Time-dependent polynomials with one multiple root and new solvable dynamical systems
Mathematical Physics
2019-10-23 v1 Classical Analysis and ODEs
Dynamical Systems
math.MP
Abstract
A time-dependent monic polynomial in the z variable with N distinct roots such that exactly one root has multiplicity m>=2 is considered. For k=1,2, the k-th derivatives of the N roots are expressed in terms of the derivatives of order j<= k of the first N coefficients of the polynomial and of the derivatives of order j<= k-1 of the roots themselves. These relations are utilized to construct new classes of algebraically solvable first order systems of ODEs as well as N-body problems. Multiple examples of solvable isochronous (all solutions are periodic with the same period) 2- and 3-body problems are provided.
Cite
@article{arxiv.1808.00512,
title = {Time-dependent polynomials with one multiple root and new solvable dynamical systems},
author = {Oksana Bihun},
journal= {arXiv preprint arXiv:1808.00512},
year = {2019}
}