Solvable Dynamical Systems in the Plane with Polynomial Interactions
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Publication:5164764
DOI10.1017/9781108773287.006zbMATH Open1483.37073arXiv1904.02151OpenAlexW2930485361MaRDI QIDQ5164764
Publication date: 12 November 2021
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.
Full work available at URL: https://arxiv.org/abs/1904.02151
Explicit solutions, first integrals of ordinary differential equations (34A05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)
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