Quantum Dynamics: Models and Mathematics pp 221-239 | Cite as

# The Lorenz Attractor and the Problem of Turbulence

Conference paper

## Abstract

Turbulence in the flow of liquids is a fascinating phenomenon. This may partly explain the conceptual confusion which exists in the scientific literature as to the nature of this phenomenon. My own opinion, and that of some other people, is that turbulence at low Reynolds numbers corresponds to a mathematical phenomenon observed in the study of solutions of differential equations The equation just written has to be understood as a time evolution equation in several dimensions. The mathematical phenomenon referred to is that in many cases, solutions of (1) have an asymptotic behavior when t → ∝ which appears erratic, chaotic, “turbulent”, and the solutions depend in a sensitive manner on initial condition.

$${{dx} \mathord{\left/
{\vphantom {{dx} {dt = X\left( x \right)}}} \right.
\kern-\nulldelimiterspace} {dt = X\left( x \right)}}$$

(1)

## Keywords

Steady State Solution Unstable Manifold Time Correlation Function Sensitive Dependence Lebesgue Measure Zero
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