Hausdorff dimension of Furstenberg-type sets associated to families of affine subspaces

Fractal sets and Hausdorff dimension

We consider Farey series of rational numbers in terms of fractal sets labeled by the Hausdorff dimension with values defined in the interval 1 < h < 2 and associated with fractal curves. Our results come from the observation that the fractional quantum Hall effect-FQHE occurs in pairs of dual topological quantum numbers, the filling factors. These quantum numbers obey some properties of the Far...

Explicit Bounds for the Hausdorff Dimension of Certain Self-Affine Sets

A lower bound of the Hausdorff dimension of certain self-affine sets is given. Moreover, this and other known bounds such as the box dimension are expressed in terms of solutions of simple equations involving the singular values of the affinities. Keyword Codes: G.2.1;G.3

Calculating Hausdorff Dimension of Julia Sets and Kleinian Limit Sets

Hausdorff Dimension of Boundaries of Self-affine Tiles in R

We present a new method to calculate the Hausdorff dimension of a certain class of fractals: boundaries of self-affine tiles. Among the interesting aspects are that even if the affine contraction underlying the iterated function system is not conjugated to a similarity we obtain an upperand and lower-bound for its Hausdorff dimension. In fact, we obtain the exact value for the dimension if the ...

The Hausdorff Dimension of the Projections of Self-affine Carpets

We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if Λ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of Λ in a non-principal direction has Hausdorff dimension min(γ, 1), where γ is the Hausdorff dimension of Λ. This gener...