stability, nonlinear viscoelasticity, Lyapunov function, strange attractor. 

The questions of finite disturbance stability of nonlinear viscoelastic solids are considered. The stability condition is a positivity of the Lyapunov function for the disturbed system. It is obtained the dimension of the strange attractor of the dynamic system that allows limiting the number of summands in Bubnov-Galerkin series. 

Sumin, Alexander Ivanovich Doctor of physical and mathematical sciences, Professor, head of Chair of mathematics, Military educational scientific center of Military and air forces "Military and air academy of a name of Professor N. E. Zhukovsky and Yu. A. Gagarin" , Voronezh