Computing with Polynomial Ordinary Differential Equations

@article{Bournez2016ComputingWP,
title={Computing with Polynomial Ordinary Differential Equations},
author={O. Bournez and D. Graça and A. Pouly},
journal={ArXiv},
year={2016},
volume={abs/1601.05683}
}

In 1941, Claude Shannon introduced the General Purpose Analog Computer(GPAC) as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later one electronic) machines of that time.
Following Shannon's arguments, functions generated by GPACs must be differentially algebraic. As it is known that some computable functions like Euler's $\Gamma(x)=\int_{0}^{\infty}t^{x-1}e^{-t}dt$ or Riemann's Zeta function $\zeta(x)=\sum_{k=0}^\infty… CONTINUE READING