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Let k[X]=k[x0,…,xn−1] and k[Y]=k[y0,…,yn−1] be the polynomial rings in n⩾3 variables over a field k of characteristic zero containing the n-th roots of unity. Let d be the cyclotomic derivation of k[X], and let Δ be the factorisable derivation of k[Y] associated with d, that is, d(xj)=xj+1 and Δ(yj)=yj(yj+1−yj) for all j∈Zn. We describe polynomial constants and rational constants of these derivations...
We present some general properties of the field of constants of monomial derivations of k(x1,…,xn), where k is a field of characteristic zero. The main result of this paper is a description of all monomial derivations of k(x,y,z) with trivial field of constants. In this description a crucial role plays the classification result of Moulin Ollagnier for Lotka–Volterra derivations with strict Darboux...
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