Polynomial algebra of constants of the Lotka-Volterra system
Volume 81 / 1999
Colloquium Mathematicum 81 (1999), 263-270
DOI: 10.4064/cm-81-2-263-270
Abstract
Let k be a field of characteristic zero. We describe the kernel of any quadratic homogeneous derivation d:k[x,y,z] → k[x,y,z] of the form $d = x(Cy+z)\frac{∂}{∂x} + y(Az+x)\frac{∂}{∂y} + z(Bx+y)\frac{∂}{∂z}$, called the Lotka-Volterra derivation, where A,B,C ∈ k.
