Lyapunov Dimension Formulas
for Lorenz-Like Systems

Corresponding Member of the RAS G. A. Leonov

Received February 29, 2016

Abstract—A general formula for the Lyapunov dimension of attractors of the Lorenz and Tigan systems is
derived in the case when all their equilibrium states are hyperbolic. Lyapunov dimension formulas are obtained
for the classical Lorentz parameters > 0, r > 1, and b (0, 4]. The problems of deriving analytical dimension
formulas for the Chen and Lu systems and for the global stability of the Lorenz system are formulated.

DOI: 10.1134/S1064562416030285

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