Estimate of the chaotic regions of the spin-axis dynamics for the Earth, where the long-term orbital dynamics is approximated by the Lagrange-Laplace system. The same colour code as Fig. 3 is used. Left panel: the complete set of initial conditions is used (same as Fig. 3, bottom row). Right panel: the orbital elements (I, ϖ, Ω) are assumedto be unknown for all planets while the remaining ones are taken from Bretagnon (1982). Accordingly, the coefficients (E_k, S_k) of the quasi-periodic series are maximised according to the estimated AMD value (see Sect. 3.2).