66 citations · 329 across the 36 of their papers we have counts for
22 papers · 1 filter
On a family of Self-Affine IFS whose attractors have a non-fractal top
Kevin G. Hare, Nikita Sidorov
Let and . In this note we prove that for the vast majority of such parameters the top of the attractor of the IFS is th…
An infinitely generated self-similar set with positive Lebesgue measure and empty interior
Simon Baker, Nikita Sidorov
Peres and Solomyak asked the question: Do there exist self-similar sets with positive Lebesgue measure and empty interior? This question was answered in the affirmative by Csörnyei…
Open maps: small and large holes with unusual properties
Kevin G. Hare, Nikita Sidorov
Let be a two-sided subshift on a finite alphabet endowed with a mixing probability measure which is positive on all cylinders in . We show that there exist arbitrarily small…
The baker's map with a convex hole
Lyndsey Clark, Kevin G. Hare, Nikita Sidorov
We consider the baker's map on the unit square and an open convex set which we regard as a hole. The survivor set is defined as the set of all…
A lower bound for the dimension of Bernoulli convolutions
Kevin G. Hare, Nikita Sidorov
Let and let denote Garsia's entropy for the Bernoulli convolution associated with . In the present paper we show that for all an…
Multidimensional self-affine sets: non-empty interior and the set of uniqueness
Kevin G. Hare, Nikita Sidorov
Let be a contracting matrix. In this paper we consider the self-affine iterated function system , where is a cyclic vector. Our main result is a…