Zobrazeno 1 - 10
of 85
pro vyhledávání: '"Savchuk, Dmytro"'
We propose self-similar contracting groups as a platform for cryptographic schemes based on simultaneous conjugacy search problem (SCSP). The class of these groups contains extraordinary examples like Grigorchuk group, which is known to be non-linear
Externí odkaz:
http://arxiv.org/abs/2408.14355
Autor:
Baker, Krystofer, Savchuk, Dmytro
We construct explicit finite generating sets for the stabilizers in Thompson's group $F$ of rational points of a unit interval or a Cantor set. Our technique is based on the Reidemeister-Schreier procedure in the context of Schreier graphs of such st
Externí odkaz:
http://arxiv.org/abs/2401.00404
Autor:
Grigorchuk, Rostislav, Savchuk, Dmytro
We canonically identify the groups of isometries and dilations of local fields and their rings of integers with subgroups of the automorphism group of the $(d+1)$-regular tree $\widetilde T_{d+1}$, where $d$ is the residual degree. Then we introduce
Externí odkaz:
http://arxiv.org/abs/2312.05427
Autor:
Savchuk, Dmytro M.
This dissertation is devoted to various aspects of groups generated by automata. We study particular classes and examples of such groups from different points of view. It consists of four main parts. In the first part we study Sushchansky p-groups in
Externí odkaz:
http://hdl.handle.net/1969.1/ETD-TAMU-2009-08-2934
Autor:
Grigorchuk, Rostislav, Savchuk, Dmytro
The ring $\mathbb Z_d$ of $d$-adic integers has a natural interpretation as the boundary of a rooted $d$-ary tree $T_d$. Endomorphisms of this tree (i.e. solenoid maps) are in one-to-one correspondence with 1-Lipschitz mappings from $\mathbb Z_d$ to
Externí odkaz:
http://arxiv.org/abs/2006.02316
Autor:
Ahmed, Elsayed, Savchuk, Dmytro
We construct a 4-state 2-letter bireversible automaton generating the lamplighter group $(\mathbb Z_2^2)\wr\mathbb Z$ of rank two. The action of the generators on the boundary of the tree can be induced by the affine transformations on the ring $\mat
Externí odkaz:
http://arxiv.org/abs/1802.03695
Autor:
Ahmed, Elsayed, Savchuk, Dmytro
We show that every polynomial in $\mathbb Z[x]$ defines an endomorphism of the $d$-ary rooted tree induced by its action on the ring $\mathbb Z_d$ of $d$-adic integers. The sections of this endomorphism also turn out to be induced by polynomials in $
Externí odkaz:
http://arxiv.org/abs/1711.06735
Autor:
Savchuk, Dmytro M., Sidki, Said N.
We introduce a class of automorphisms of rooted $d$-regular trees arising from affine actions on their boundaries viewed as infinite dimensional vector spaces. This class includes, in particular, many examples of self-similar realizations of lampligh
Externí odkaz:
http://arxiv.org/abs/1510.08434
Autor:
Grigorchuk, Rostislav, Savchuk, Dmytro
We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree associated with th
Externí odkaz:
http://arxiv.org/abs/1412.8020
We introduce a new tool, called the orbit automaton, that describes the action of an automaton group $G$ on the subtrees corresponding to the orbits of $G$ on levels of the tree. The connection between $G$ and the groups generated by the orbit automa
Externí odkaz:
http://arxiv.org/abs/1411.0158