$$
\dot{x} = \sigma (y-x) \
\dot{y} = rx - y - xz \
\dot{z} = xy - bz \
\sigma, r, b > 0
$$
- Prandtl number $\sigma$ is the ratio of the viscous to thermal diffusion,
- Rayleigh umber $r$ is the ration of the driving to dissipation,
- $b$ has no name
- Lorenz system cannot have repellers - they are sources of volume
any positive (largest) lyapunov exponent => chaotic
- always can embed trajectory between 2 trajectories - infinite space