arXiv subjects

Dmitry Vaulin

Publications and source records attributed to Dmitry Vaulin.

4 recordsLinked to original sources

arXiv2017

On dendrites, generated by polyhedral systems and their ramification points

The paper considers systems of contraction similarities in $\mathbb R^d$ sending a given polyhedron $P$ to polyhedra $P_i\subset P$, whose non-empty intersections are singletons and contain the common vertices of those polyhedra, while the intersection hypergraph of the system is acyclic. It is proved that the attractor $K$ of such system is a dendrite in $\mathbb R^d$. The ramification points of such dendrite fave finite order whose upper bound depends only on the polyhedron $P$, and the set of the cut points of the dendrite $K$ is equal to the dimension of the whole $K$ iff $K$ is a Jordan arc.

math.MG↗

arXiv2017

Self-Similar Dendrites Generated by Polygonal Systems in the Plane

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.

math.MG↗

arXiv2016

Self-Similar Jordan Arcs Which Do Not Satisfy OSC

It was proved in 2007 by C.Bandt and H.Rao that if a system $S = \{S_1 , ..., S_m \}$ of contraction similarities in $R^2$ with a connected attractor $K$ has the finite intersection property, then it satisfies OSC. We construct a self-simiilar Jordan arc in $R^3$, defined by a system $S$ , which does not satisfy OSC and at the same time has one-point intersection property.

math.MG↗

arXiv2014

On two classes of dense 2-generator subgroups in $\mathbb C$

We consider dense 2-generator multiplicative subgroups in $\mathbb C$ and show that for each point $z\in \mathbb C$ the set of limit values for the arguments of the powers of each generator at the point $z$ is either finite or is $[-π,π]$

math.DS↗