Cantor Sets with Complicated Geometryand

Cantor Sets with Complicated Geometry and Modeled by General Symbolic Dynamics

We analyze the structure and the regularity of a broad class of Cantor sets. We provide criteria, and non-trivial examples of regularity and of non-regularity, exhibiting new phenomena in dimension theory. We show that a Cantor set constructed with rectangles can be reduced to one constructed with aligned rectangles, having equal Hausdorr and box dimensions. This is proved showing the existence...

Dimension of Cantor Sets with Complicated Geometry

The approximate solutions of Fredholm integral equations on Cantor sets within local fractional operators

In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools ...

One-dimensional Schrödinger Operators with Δ′-interactions on Cantor-type Sets

We introduce a novel approach for defining a δ′-interaction on a subset of the real line of Lebesgue measure zero which is based on Sturm– Liouville differential expression with measure coefficients. This enables us to establish basic spectral properties (e.g., self-adjointness, lower semiboundedness and spectral asymptotics) of Hamiltonians with δ′-interactions concentrated on sets of complica...

Distinguishing Bing-whitehead Cantor Sets

Bing-Whitehead Cantor sets were introduced by DeGryse and Osborne in dimension three and greater to produce examples of Cantor sets that were non standard (wild), but still had simply connected complement. In contrast to an earlier example of Kirkor, the construction techniques could be generalized to dimensions bigger than three. These Cantor sets in S are constructed by using Bing or Whitehea...