Epicyclic frequencies ω_± (solid lines) and critical frequency ω_c (dashed line) for m = 1 and (a) Ω₀/f = 3 and (b) Ω₀/f = −2. The gray area denotes the region where the solution is wave-like (i.e., Δ < 0), while the white area is the evanescent region (i.e., Δ > 0). Dotted lines represent frequencies ω_r for neutral modes in the upper (cases I and IV) and lower (cases II and V) branches, and for unstable modes (case III).