Geometric limit of Julia set of a family of rational functions with odd degree

Exploring parameter spaces in complex dynamics

“…As we increase the degree d, the numerical simulations that both the Julia sets and the non-escape set begin to decrease geometrically, showing in the limit (in some suitable topology) a tendency to a set limited to a ring around the unit circle. Recently, [20] studied this type of problem for Julia sets on a family of rational functions. The study on geometric limits for the non-escape locus of the Blaschke products is an open problem.…”