Lyapunov functions in the global analysis of chaotic systems
AbstractWe 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.
How to Cite
Leonov, G. A. “Lyapunov Functions in the Global Analysis of Chaotic Systems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 1, Jan. 2018, pp. 40-62, http://umj.imath.kiev.ua/index.php/umj/article/view/1541.