# A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function

arXiv: https://arxiv.org/abs/1803.06087 · HTML: https://mlsanity.com/paper/1803.06087/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [Analytical Lyapunov Function Discovery: An RL-based Generative Approach](https://mlsanity.com/paper/2502.02014/) (2025)

## Abstract (arXiv)

We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.