@article{Leonov_2018, title={Lyapunov functions in the global analysis of chaotic systems}, volume={70}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/1541}, abstractNote={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.}, number={1}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={LeonovG. A.}, year={2018}, month={Jan.}, pages={40-62} }