TY - JOUR
AU - G. A. Leonov
PY - 2018/01/25
Y2 - 2020/11/25
TI - Lyapunov functions in the global analysis of chaotic systems
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 70
IS - 1
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1541
AB - We present an overview of development of the direct Lyapunov method in the global analysis of chaotic systems anddescribe 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 homoclinictrajectories, and in the estimation of the dimension of attractors. The efficiency of construction of Lyapunov-type functionsis demonstrated. In particular, the Lyapunov dimension formula is proved for the attractors of the Lorentz system.
ER -