Lyapunov Dimension of Attractors of the Lorenz-Like Differential Equations

Abstract

In 1963 E.Lorenz discovered strange attractors, which correspond to the turbulence in liquids and atmosphere. In the second half of the 20-th century these attractors were described in electromechanical and electronical systems. In this time the well-known scientists created the methods of estimates of attractor dimension in the theory of dynamical systems and differential equations. Lyapunov function has been introduced in the estimates of this attractors in the last two decades. In this paper new classes of Lyapunov functions for the Lorenz-like systems are constructed and Lyapunov dimension formulas are obtained.