8 citations · 41 across the 20 of their papers we have counts for
25 papers
Characters and IRS's on branch groups and embeddings into hyperfinite factor
Artem Dudko, Rostislav Grigorchuk
Using the construction by Bencs and Tóth of invariant random subgroups on weakly branch groups acting on regular rooted trees we produce uncountably many indecomposable characters…
Lower bounds on the Hausdorff dimension of some Julia sets
Artem Dudko, Igors Gorbovickis, Warwick Tucker
We present an algorithm for a rigorous computation of lower bounds on the Hausdorff dimensions of Julia sets for a wide class of holomorphic maps. We apply this algorithm to obtain…
On spectral properties of the Schreier graphs of the Thompson group
Artem Dudko, Rostislav Grigorchuk
In this article we study spectral properties of the family of Schreier graphs associated to the action of the Thompson group on the interval [0,1]. In particular, we describe s…
On spectra of representations and graphs. Erratum
Artem Dudko, Rostislav Grigorchuk
Unfortunately the proof of the main result of [1], Theorem 1, has a flaw. Namely, Lemma 13 used in the proof of Proposition 11 is correct only under an additional assumption that t…
On computational complexity of Cremer Julia sets
Artem Dudko, Michael Yampolsky
We find an abundance of Cremer Julia sets of an arbitrarily high computational complexity.
On the question "Can one hear the shape of a group?" and Hulanicki type theorem for graphs
Artem Dudko, Rostislav Grigorchuk
We study the question of whether it is possible to determine a finitely generated group up to some notion of equivalence from the spectrum of . We show that…