Lyapunov dimension formula for the global attractor of the Lorenz system
Leonov, G. A., Kuznetsov, N., Korzhemanova, N. A., & Kusakin, D. V. (2016). Lyapunov dimension formula for the global attractor of the Lorenz system. Communications in Nonlinear Science and Numerical Simulation, 41, 84-103. https://doi.org/10.1016/j.cnsns.2016.04.032
© 2016 Elsevier B.V. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.
The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of parameters, including classical values, was analytically obtained first by G.A. Leonov in 2002. Leonov used the construction technique of special Lyapunov-type functions, which was developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters, of the system, such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values including all parameters, which satisfy the classical physical limitations.
PublisherElsevier B.V.; Peking University
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