Introducing isodynamic points for binary forms and their ratios

Abstract The isodynamic points of a plane triangle are known to be the only pair its centers invariant under action Möbius group $${\mathcal {M}}$$ M on set triangles, Kimberling (Encyclopedia Triangle Centers, http://faculty.evansville.edu/ck6/encyclopedia ). Generalizing this classical result, we introduce below map associating univariate polynomial degree $$d\ge 3$$ d ≥ 3 with at most double roots (at most) $$2d-4$$ 2 - 4 such that commutes zero loci initial and image. image will called preimage polynomial. Our construction naturally extends from polynomials binary forms further their ratios.