Level curves of the secular Hamiltonian for the current and past evolution of the object 2015 FJ₃₄₅. Three smooth trajectories are considered, divided by separatrix crossings. The constant parameter η₀ is given in Table 1, whereas 2πJ is given above the graphs (au² rad² yr^-1). The current orbital elements of 2015 FJ₃₄₅ result in the leftmost phase portrait a). Contrary to previous graphs, the secondary oscillations of the semi-secular trajectory (red curve) are noticeable. The secular trajectory (mean curve), though, follows still pretty well the level curves given by the model. Starting from the current position of 2015 FJ₃₄₅ (blue cross), the red curve is drawn until it reaches a change of the resonance topology (from a single to a double island), on the green line. Following the level curve towards the left (past evolution), the blue spot represents the position of the previous separatrix crossing undergone by 2015 FJ₃₄₅. The middle graph b) shows the secular model for the past evolution of 2015 FJ₃₄₅. The blue spot represents its position at the transition to its current state (same as graph a)). Following the level curve downwards (past evolution), the green spot shows the position of the previous separatrix crossing undergone by 2015 FJ₃₄₅. The rightmost graph c) presents the secular model for the earlier evolution of 2015 FJ₃₄₅. The green spot shows its position at the transition to the next part of the trajectory (same as graph b)). Following the level curve downwards (past evolution), the black spot is taken as initial condition for a numerical integration (see text and Fig. 5).