Symmetric quadratic dynamical systems

We will discuss the dynamical systems wich arise in classical and modern problems of mathematics, physics, mechanics and biology.
For such systems we introduce the notion of algebraical integrability. We will describe a wide class of algebraically integrable systems.
This class contains the Euler top, Kovalevskaya system, Lotka-Volterra type systems, Darboux-Halphen systems and modern generalizations of this systems.
In the talk we present results obtained recently with E. Yu. Netay (Bunkova).