17 citations · 33 across the 12 of their papers we have counts for
5 papers · 1 filter
Diophantine property of matrices and attractors of projective iterated function systems in
Boris Solomyak, Yuki Takahashi
We prove that almost every finite collection of matrices in and with positive entries is Diophantine. Next we restrict ourselves to the case $…
Sums of two self-similar Cantor sets
Yuki Takahashi
We show that for any pair of self-similar Cantor sets with sum of Hausdorff dimensions greater than 1, one can create an interval in the sumset by applying arbitrary small perturba…
On the interior of projections of planar self-similar sets
Yuki Takahashi
We consider projections of planar self-similar sets, and show that one can create nonempty interior in the projections by applying arbitrary small perturbations, if the self-simila…
Sums of two homogeneous Cantor sets
Yuki Takahashi
We show that for any two homogeneous Cantor sets with sum of Hausdorff dimensions that exceeds 1, one can create an interval in the sumset by applying arbitrary small perturbations…
Products of two Cantor sets
Yuki Takahashi
We consider products of two Cantor sets, and obtain the optimal estimates in terms of their thickness that guarantee that their product is an interval. This problem is motivated by…