Locally finite and locally nilpotent derivations with applications to polynomial flows and polynomial morphisms

van den Essen, Arno

doi:10.1090/S0002-9939-1992-1111440-5

Locally finite and locally nilpotent derivations with applications to polynomial flows and polynomial morphisms
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by Arno van den Essen PDF

Proc. Amer. Math. Soc. 116 (1992), 861-871 Request permission

Abstract:

We give a very simple proof of the fact that the Lorenz equations and the Maxwell-Bloch equations do not have a polynomial flow. We also give an algorithm to decide if a two-dimensional vector field over $\mathbb {R}$ has a polynomial flow and how to compute the solutions (in case the vector field has a polynomial flow).

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