11 citations · 25 across the 8 of their papers we have counts for
9 papers
On the set of subarcs in some non-postrcritically finite dendrites
Nikolai Abrosimov, Marina Chanchieva, Andrey Tetenov
We construct a family of non-PCF dendrites in a plane, such that in each of them all subarcs have the same Hausdorff dimension , while the set of -dimensional Hausdorff m…
On -deformations of polygonal dendrites
Dmitry Drozdov, Mary Samuel, Andrey Tetenov
We find the conditions under which the attractor of a deformation of a contractible polygonal system is a dendrite.
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…
On Dendrites Generated By Symmetric Polygonal Systems: The Case of Regular Polygons
Mary Samuel, Dmitry Mekhontsev, Andrey Tetenov
We define -symmetric polygonal systems of similarities and study the properties of symmetric dendrites, which appear as their attractors. This allows us to find the conditions u…
Self-Similar Dendrites Generated by Polygonal Systems in the Plane
Mary Samuel, Andrey Tetenov, Dmitry Vaulin
We consider a method of construction of self-similar dendrites on a plane and establish main topological and metric properties of resulting class of dendrites.
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 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…
On transverse hyperplanes to self-similar Jordan arcs
Andrey Tetenov
We consider self-similar Jordan arcs in , different from a line segment and show that they cannot be projected to a line bijectively. Moreover, we show that the set of poi…
The example of a self-similar continuum which is not an attractor of any zipper
O. Purevdorj, A. V. Tetenov
The article contains a construction of a self-similar dendryte which cannot be the attractor of any self-similar zipper.