86 citations · 574 across the 105 of their papers we have counts for
8 papers · 1 filter
Invariance property on group representations of the Cayley tree and its applications
U. A. Rozikov, F. H. Haydarov
In the present paper, we give a certain condition on subgroups of the group representation of the Cayley tree such that an invariance property holds. Except for the given condition…
Dynamics of a population with two equal dominated species
U. A. Rozikov, J. B. Usmonov
We consider a population with two equal dominated species, dynamics of which is defined by one-dimensional piecewise-continuous, two parametric functions. It is shown that for any…
Dynamics of quadratic operators generated by China's Five elements philosophy
N. N. Ganikhodjaev, C. H. Pah, U. A. Rozikov
Motivating by the China's five element philosophy (CFEP) we construct a permuted Volterra quadratic stochastic operator acting on the four dimensional simplex. This operator (depen…
-adic boundary laws and Markov chains on trees
A. Le Ny, L. Liao, U. A. Rozikov
In this paper we consider -state potential on general infinite trees with a nearest-neighbor -adic interactions given by a stochastic matrix. {We show the uniqueness of the a…
Dynamical systems of the -adic -rational functions with two fixed points
U. A. Rozikov, I. A. Sattarov
We consider a family of -rational functions given on the set of complex -adic field . Each such function has the two distinct fixed points …
On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field
Leonid V. Bogachev, Utkir A. Rozikov
The paper concerns the -state Potts model (i.e., with spin values in ) on a Cayley tree of degree (i.e., with edges emanating from…