5. Statistical properties

To date, the geometry of Lorenz dynamic model trajectories has been studied in some detail. Two important properties have been observed:

1. The trajectories are attracted to a fractal set (of dimension 2,04...) called a strange attractor. $\mathcal{A}$  ;

2. On this attractor, trajectories have the property of being sensitive to initial conditions: two points that are initially very close will generally have trajectories that diverge at an exponential rate.

This last property gives a "chaotic" appearance to the trajectories, and we now wish to describe these observational properties in more detail. We call them "statistical properties of the dynamical system", because they will...