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Lyapunov dimension formulas for Lorenz-like systems

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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 σ > 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.

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Authors and Affiliations

  1. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, V. O., Bol’shoi pr. 61, St. Petersburg, 199178, Russia

    G. A. Leonov

  2. Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetskii pr. 28, Peterhof, St. Petersburg, 198504, Russia

    G. A. Leonov

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  1. G. A. Leonov
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Correspondence to G. A. Leonov.

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Original Russian Text © G.A. Leonov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 468, No. 5, pp. 496–498.

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Leonov, G.A. Lyapunov dimension formulas for Lorenz-like systems. Dokl. Math. 93, 304–306 (2016). https://doi.org/10.1134/S1064562416030285

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  • DOI: https://doi.org/10.1134/S1064562416030285

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