3 citations · 3 across the 3 of their papers we have counts for
5 papers
On weak separation property for self-affine Jordan arcs
Andrei Tetenov, Olesya Chelkanova
We consider self-affine arcs in and prove that violation of "inner" weak separation property for such arcs implies that the arc is a parabolic segment. Therefore, if…
On the connected components of fractal cubes
Dmitry Drozdov, Andrei Tetenov
We show that a fractal cube in may have an uncountable set of connected components neither of which is contained in any plane, whereas the set is a…
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…
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…
On dendrites, generated by polyhedral systems and their ramification points
Andrei Tetenov, Mary Samuel, Dmitry Vaulin
The paper considers systems of contraction similarities in sending a given polyhedron to polyhedra , whose non-empty intersections are singletons an…