3 citations · 8 across the 11 of their papers we have counts for
11 papers · 1 filter
Self-similar dendrites with finite boundary and P-sprouts
Andrei Tetenov, Ivan Yudin, Dmitrii Drozdov
Each self-similar dendrite K with a finite self-similar boundary defines a finite acyclic edge-labeled bipartite graph G, called the sprout of K. The paper shows that the sprout G…
On metric properties of self-affine polygonal dendrites
Andrei Tetenov, Ivan Yudin, Dilmurat Kutlimuratov
We prove that for any self-affine dendrite K generated by a polygonal system, there are constants C>0 and such that for any x, y in K, the Jordan arc in K with end…
On the intersection of fractal cubes
Andrei Tetenov, Dmitry Drozdov
We consider the intersections of fractal k-cubes of order n and intersections of their respective opposite l-faces. The main result of the paper is the theorem on representation of…
On the classification of fractal square dendrites
Dmitry Drozdov, Andrei Tetenov
We consider the classification of fractal square dendrites based on the types of the self-similar boundary and the main tree of such dendrites. We show that th…
On bi-Lipschitz isomorphisms of self-similar Jordan arcs
Ilya Galai, Andrei Tetenov
We find the conditions for bi-Lipschitz equivalence of self-similar Jordan arcs which are the attractors of self-similar zippers.
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…
Finiteness properties for self-similar continua
Andrei Tetenov
We consider self-similar continua possessing finite intersection property and prove intersection graph criterion for self-similar dendrites, finite order Theorem for such continua…
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…