Trajectory of Jupiter’s spin axis in the vicinity of resonance with the fourth harmonics of ζ (see Table 2). Being farther away from Jupiter’s precession frequency, the contribution of other harmonics can be averaged; their mean contribution is included here up to third order in the amplitudes (as in Eq. (17) of Saillenfest et al. 2019). Each trajectory corresponds to a level curve of the Hamiltonian, which has only one degree of freedom. The red dot shows the current location of Jupiter, and the black dot shows Cassini state 2. The red curve is the current trajectory of Jupiter’s spin axis for λ = 0.250 (top) or λ = 0.237 (bottom).