The Lyapunov dimension formula for the global attractor of the Lorenz system

Abstract

The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions 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, which include all parameters satisfying the classical physical limitations. One of the motivation of this work is the possibility of computing a chaotic attractor in the Lorenz system in the case of one unstable and two stable equilibria.

arXiv admin note: text overlap with arXiv:1505.04729

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• A short survey on Lyapunov dimension for finite dimensional dynamical systems in Euclidean space
• Time-delay control for stabilization of the Shapovalov mid-size firm model
• Variational description of uniform Lyapunov exponents via adapted metrics on exterior products
• Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents
• A lower-bound estimate of the Lyapunov dimension for the global attractor of the Lorenz system