Birkhoff-recurrent solutions to algebraic equations

The paper considers algebraic equations whose coefficients are continuous functions given on a connected topological group. It is proven that if the vector function made up of the coefficients is recurrent in the sense of Birkhoff and if the discriminant of the equation never vanishes, then each continuous solution is recurrent. The proof is based on the theory of extensions of dynamic systems.Translated from Matematicheskie Zametki, Vol. 12, No. 4, pp. 617–623, April, 1973.