Abstract
We show that any homogeneous polynomial solution of the eiconal type equation $$|\nabla F(x)|^2=m^2|x|^{2m-2}$$ , $$m\ge 1$$ , is either a radially symmetric polynomial $$F(x)=\pm |x|^{m}$$ (for even $$m$$ ’s) or it is a composition of a Chebychev polynomial and a Cartan–Münzner polynomial.
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