In this Letter, the analytical expression of topological Hausdorff dimension D t H is derived
for some kinds of infinitely ramified Sierpiński carpets. Furthermore, we deduce that the …

Mean geodesic distance of the level-n Sierpinski gasket - ScienceDirect Skip to main contentSkip
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A carpet is a metric space homeomorphic to the Sierpiński carpet. We characterize, within a
certain class of examples, non-self-similar carpets supporting curve families of nontrivial …

Manhattan property of geodesic paths on self-affine carpets Page 1 Arch. Math. 111 (2018),
279–285 c© 2018 Springer International Publishing AG, part of Springer Nature 0003-889X/18/030279-7 …

For the Sierpinski-like sponge in R n, we obtain the Hausdorff dimension of the set of
differentiable points such that there exists an (n− 1)-rectifiable subsurface which has a …

We identify a collection of periodic billiard orbits in a self-similar Sierpiński carpet billiard
table Ω (S a). Based on our refinement of the result of Durand-Cartagena and Tyson …

In a 2013 paper, Cheeger and Kleiner introduced a new type of dimension for metric spaces,
the" Lipschitz dimension". We study the dimension-theoretic properties of Lipschitz …

In this paper, we study geodesics in the Sierpinski carpet and Menger sponge, as well as in
a family of fractals that naturally generalize the carpet and sponge to higher dimensions. In …

If D is a rational polygon, then the associated rational billiard table is given by\Omega (D).
Such a billiard table is well understood. If F is a closed fractal curve approximated by a …

We present an introduction to the area of computability in dynamical systems. One of the
central questions in this area is if relevant dynamical objects can be algorithmically …