16 citations · 27 across the 2 of their papers we have counts for
3 papers
math.DS2008
Quasisymmetric conjugacy between quadratic dynamics and iterated function systems
Kemal Ilgar Eroğlu, Steffen Rohde, Boris Solomyak
We consider linear iterated function systems (IFS) with a constant contraction ratio in the plane for which the "overlap set" $\Ok$ is finite, and which are "invertible" on the att…
math.CA2006★ 16 cited
On the arithmetic sums of Cantor sets
Kemal Ilgar Eroglu
Let $C_\la$ and $C_\ga$ be two affine Cantor sets in with similarity dimensions $d_\la$ and $d_\ga$, respectively. We define an analog of the Bandt-Graf condition for…
math.CA2006★ 11 cited
On planar self-similar sets with a dense set of rotations
Kemal Ilgar Eroglu
We prove that if is a planar self-similar set with similarity dimension whose defining maps generate a dense set of rotations, then the -dimensional Hausdorff measure of…