arXiv subjects

Konstantin M. Posadskiy

Publications and source records attributed to Konstantin M. Posadskiy.

2 recordsLinked to original sources

arXiv2026

On a family of non-coset 2-valued groups

Within an important class of discrete-time 2-valued dynamical systems on $\mathbb{C}$ defined by polynomials, we extract a family of systems induced by the action of a 2-valued group. We study this 2-valued group and its analogues obtained by replacing $\mathbb{C}$ with an arbitrary field $F$. We establish that all of them are double coset groups. For some of them we prove non-cosetness. In the case $F = \mathbb{C}$, this yields the first example of a topologically non-coset, non-discrete topological 2-valued group.

math.GR↗

arXiv2025

Continuous two-valued discrete-time dynamical systems and actions of two-valued groups

We study continuous 2-valued dynamical systems with discrete time (dynamics) on $\mathbb{C}$. The main question addressed is whether a 2-valued dynamics can be defined by the action of a 2-valued group. We construct a class of strongly invertible continuous 2-valued dynamics on $\mathbb{C}$ such that none of these dynamics can be given by the action of any 2-valued group. We also construct an example of a continuous 2-valued dynamics on $\mathbb{C}$ that is not strongly invertible but can be defined by the action of a 2-valued group.

math.GR↗