10 citations · 15 across the 4 of their papers we have counts for
6 papers
General position theorem and its applications
Vladislav Aseev, Kirill Kamalutdinov, Andrei Tetenov
We introduce some general and special formulations of general position theorem for parametrized families of fractals and explain the techniques of its application to prove the exis…
Even unique intersection point can break OSC: an example
Kirill Kamalutdinov, Andrey Tetenov
This was a long-standing question since 90-ies whether one-point intersection property for a self-similar set implies open set condition. We answer this question negatively. We giv…
Twofold Cantor sets in R
Kirill Kamalutdinov, Andrei Tetenov
We introduce a class of self-similar sets which we call {\em twofold Cantor sets} in which are totally disconnected, do not have weak separation property and a…
Self-Similar Jordan Arcs Which Do Not Satisfy OSC
Andrey Tetenov, Kirill Kamalutdinov, Dmitry Vaulin
It was proved in 2007 by C.Bandt and H.Rao that if a system of contraction similarities in with a connected attractor has the finite intersectio…
On the morphisms of fractal curves that increase their smoothness
Kirill Kamalutdinov, Svetlana Sorokina
We propose a construction which transforms a self-similar zipper in to a self-affine zipper whose attractor is a smooth curve.
On two classes of dense 2-generator subgroups in
Kirill Kamalutdinov, Andrey Tetenov, Dmitry Vaulin
We consider dense 2-generator multiplicative subgroups in and show that for each point the set of limit values for the arguments of the powers of each…