Start with, for example, the Lorenz system
$$\begin{align} \frac{\mathrm{d}x}{\mathrm{d}t} &= \sigma (y - x), \\[6pt] \frac{\mathrm{d}y}{\mathrm{d}t} &= x (\rho - z) - y, \\[6pt] \frac{\mathrm{d}z}{\mathrm{d}t} &= x y - \beta z. \end{align}$$
- any references which have general techniques for (computing the jet groups)/(identifying which Lie groups they are) of this (or similar) system(s) (or)
- worked computation for this system
(the systems that I eventually want to apply this computation to are in Julien Clint Sprott's Strange Attractors: Creating Patterns in Chaos, ch6. p322)