Том 70
№ 6

All Issues

Leonov G. A.

Articles: 1
Article (Russian)

Lyapunov functions in the global analysis of chaotic systems

Leonov G. A.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 40-62

We present an overview of development of the direct Lyapunov method in the global analysis of chaotic systems and describe three directions in which the Lyapunov functions are applied: in the methods of localization of global attractors, where the estimates of dissipativity in a sense of Levinson are obtained, in the problems of existence of homoclinic trajectories, and in the estimation of the dimension of attractors. The efficiency of construction of Lyapunov-type functions is demonstrated. In particular, the Lyapunov dimension formula is proved for the attractors of the Lorentz system.