Phase space in which K2-19 b,c reside. Left panel: our posterior values of the real and imaginary parts of u (7000 pink points using Eq. (6)); a complete resonant cycle starting from the MAP value of u (black curve); the associated primary fixed point for which u = R (cyan star) and the secondary and hyperbolic fixed points (orange and blue stars, respectively, these two only exist when the phase space is resonant); the associated separatrix (red curve); a complete resonant cycle using the system parameters of Petigura et al. (2020) for the initial value of u (gray curve); and the associated separatrix, which is almost identical to ours (purple curve). Right panel: our posterior values of the real and imaginary parts of v (7000 light blue points using Eq. (7)); a complete supercycle starting from the MAP value of v (black curve) and the system parameters of Petigura et al. (2020) (gray curve). Each panel uses different scales.