Generalized -Attractor Models from Elementary Hyperbolic Surfaces

Figure 16

The potentials and on the annulus of modulus (, ). For and , we indicate only the dependence of , since these two potentials do not depend on the polar angle . Notice that tends to its infimum at the inner funnel end, while tends to its infimum at the outer funnel end. Similarly, and tend to their suprema at opposite funnel ends.

(a) Plot of (blue) and (orange) as functions of for . The values and correspond to the two funnel ends of

(b) Level plot of on for . Darker tones indicate lower values of . In this case, the maximum of is located at , while the minimum is located at