Fractional Densities for the Wada Basins

Abstract

Fractional density for basis zero Schnirelmann density has been defined. Definition of the fractional density is similar to the Hausdorff-Besicovitch dimension. The existence of the basis zero Schnirelmann density for every Wada basin (Wada ocean) earlier has been proved. This means every Wada basin/ocean are quite topologically characterized to be fractional density. Therefore all fractional densities are invariant with respect to a plane homeomorphism.