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

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. Citation Submitted for publication Article Download View A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function