The Lorenz attractor
Fractal Geometry

Article REF: AF218 V1

The Lorenz attractor
Fractal Geometry

Author : Jean-Charles PINOLI

Publication date: October 10, 2017 | Lire en français

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23. The Lorenz attractor

Lorenz's physical system (or oscillator) is represented by a mathematical system of three ordinary differential equations, studied in 1963 as a three-dimensional mathematical model for terrestrial atmospheric convection (simplified with respect to the Navier-Stokes partial differential equations used in fluid mechanics):

{\begin{matrix} \frac{d x}{d t} = σ (y - x), \\ \frac{d y}{d t} = x (ρ - z) - y, \end{matrix}

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Bibliography

(1) - AARTS (J.M.), NISHIURA (T.) - Dimension and extensions, - North-Holland, 331 pages (1993).
(2) - ALBEVERIO (S.), PRATSIOVYTYL (M.), TORBIN (G.) - Transformations preserving the Hausdorff-Besicovitch dimension, - Central European Journal...

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