Solvable Dynamical Systems in the Plane with Polynomial Interactions
Abstract
In this paper we report a few examples of algebraically solvable dynamical systems characterized by 2 coupled Ordinary Differential Equations which read as follows: x_n = P(n) (x1, x2) , n = 1, 2 , with P(n) (x1, x2) specific polynomials of relatively low degree in the 2 dependent variables x1 = x1 (t) and x2 = x2 (t) . These findings are obtained via a new twist of a recent technique to identify dynamical systems solvable by algebraic operations, themselves explicitly identified as corresponding to the time evolutions of the zeros of polynomials the coefficients of which evolve according to algebraically solvable (systems of) evolution equations.
Cite
@article{arxiv.1904.02151,
title = {Solvable Dynamical Systems in the Plane with Polynomial Interactions},
author = {Francesco Calogero and Farrin Payandeh},
journal= {arXiv preprint arXiv:1904.02151},
year = {2019}
}
Comments
11 pages, Sabmitted 27 August 2018, to be published as a chapter in a collective book to celebrate the 65th birthdate of Emma Previato (in press)