14 citations
4 papers
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…
Physical Principles of the Amplification of Electromagnetic Radiation Due to Negative Electron Masses in a Semiconductor Superlattice
A. V. Shorokhov, M. A. Pyataev, N. N. Khvastunov +3
In a superlattice placed in crossed electric and magnetic fields, under certain conditions, the inversion of electron population can appear at which the average energy of electrons…
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.