Various dynamical quantities of the loL stars (left column) and hiL stars (middle column) and subclump stars (right column) in a potential with a triaxial halo with a range of p and q as calculated by AGAMA for an integration time of 100 Gyr. The grey horizontal line at p = 1 serves to guide the eye and indicates axisymmetric potentials. The white dotted line indicates the Ω_ϕ : Ω_z = 1:1 resonance (see also bottom row). Top row: average Lyapunov exponent. A non-zero Lyapunov exponent indicates that there is chaoticity. The overlaid black contours, which are also shown in the other rows, map average(Λ_*) at the levels of 0.02 and 0.04, as is also indicated on the colourbar. Second row: median variation in L_z, with ΔL_z,* = max(L_z,*) − min(L_z,*) over the entire integration time. Third row: median variation in L_y, with ΔL_y,* = max(L_y,*) − min(L_y,*) over the entire integration time. Bottom row: median(Ω_ϕ : Ω_z) ratio. We can see clear correspondences between the four different rows. The chaotic regions overlap with the median(Ω_ϕ : Ω_z) = 1:1 resonance and a transition in the value of ΔL_z and ΔL_y. This transition indicates a change in orbit family, and the text in the middle column indicates where the different orbit families reside, of which examples are shown in Fig. 5 (the crosses in this figure indicate their p and q). To the left of the chaotic band we find z-tube orbits, which have an oscillating L_y and a roughly conserved L_z, such that median(ΔL_y) ≲ 4000 kpc km s⁻¹, median(ΔL_z) ≲ 500 kpc km s⁻¹. To the right of the chaotic band we find y-tube orbits, which have a roughly conserved L_y and an oscillating L_z, such that median(ΔL_y) ~ 1000 kpc km s⁻¹ and median(Δ L_z) ~ 3000 kpc km s⁻¹. For p > 1, the Ω_ϕ:Ω_z = 1:1 is a resonance that traps orbits, which reduces their variation in both L_y and L_z. This is most clear for the subclump stars.