Isocontours of the averaged perturbative potentials in the e–ω space for several different settings. The perturbing potential is due to an infinitesimally thin ring of radius ﹩{R}_{{\rm{d}}}﹩ in panels (A) through (C); in panel (D) the perturbing potential is a superposition of potentials of a ring and a spherical cluster with radial density profile ﹩\varrho (r)\propto {r}^{-7/4}﹩ and mass ﹩{M}_{{\rm{c}}}=1.5{M}_{{\rm{d}}}﹩ within the radius ﹩{R}_{{\rm{d}}}﹩. In panels (E) and (F) the source of the perturbing potential is a razor-thin disk of constant surface density and outer radius ﹩{R}_{{\rm{d}}}﹩. Specific values of orbit semimajor axis, a, and the Kozai integral, c, are as follows: (A): ﹩a=0.48\;{R}_{{\rm{d}}},\ c=0.85;\;﹩ (B): ﹩a=0.48\;{R}_{{\rm{d}}},\ c=0.5;\;﹩ (C): ﹩a=1.50\;{R}_{{\rm{d}}},\ c=0.85;\;﹩ (D): ﹩a=0.48\;{R}_{{\rm{d}}},\ c=0.5;\;﹩ (E): ﹩a=0.48\;{R}_{{\rm{d}}},\ c=0.85;\;﹩ (F): ﹩a=0.48\;{R}_{{\rm{d}}},\ c=0.1﹩. The dashed line in panel C corresponds to orbits that intersect the perturbing ring. Note the different ranges of the boxes in the upper and lower panels, which reflect different maxima of eccentricity for different values of c.