Abstract:

If a function , where and (Riemann Sphere), then there exists a set defined to be Julia such that:

and its Hausdorff dimension contains a known bound if in the logistic family. A detailed analysis was performed using bounding maps that are considered an extension of commonly known sets, with all residing outside of the quadratic family: . We present a Hausdorff dimension bound, along with further topological inferences relating to connectivity and density. The applications of this include a deeper innate understanding of logical Hilbert subspace characterization.