Viktor Buchstaber

We will consider the classical heat equation and discuss its relations with classical and modern differential equations and dynamical systems that naturally appear in problems of mechanics, physics and mathematics. In the focus of our interest will be a new notion of n-solutions of the heat equation. For each n = 0 ; 1 ; 2 ; 3 ; : : : the n-solutions are defined by solutions of a non-linear ordinary differential equation of order n + 1 on the base of a polynomial dynamical system in the n-dimensional space. The talk is based on recent results obtained jointly with E. Netay.