arXiv subjects

Mehrnaz Pourattar

Publications and source records attributed to Mehrnaz Pourattar.

4 recordsLinked to original sources

arXiv2025

Compact non-uniformizable Li-Yorke chaotic dynamical systems via an example

The main aim of this paper is extending the concept of scambled pair and Li--Yorke chaos to non--uniform compact dynamical systems. We show for finite (compact Alexandroff) topological space $X$ with at least two elements the following statements are equivalent: $\bullet$ one--sided shift $σ:X^{\mathbb{N}}\to X^\mathbb{N}$ is Li--Yorke chaotic, $\bullet$ one--sided shift $σ:X^{\mathbb{N}}\to X^\mathbb{N}$ has at least one scrambled pair, $\bullet$ one--sided shift $σ:X^{\mathbb{N}}\to X^\mathbb{N}$ has at least one non--asymptotic pair, $\bullet$ there exists $a,b\in X$ such that $\overline{\{a\}}\cap\overline{\{b\}}=\varnothing$, $\bullet$ $\bigcap\{\overline{\{a\}}:a\in X\}=\varnothing$.

math.DS↗

arXiv2025

Closed graph property and Khalimsky spaces

In the following text for Khalimsky $n-$dimensional space $\mathcal{K}^n$ we show self--map $f:\mathcal{K}^n\to\mathcal{K}^n$ has closed graph if and only if there exist integers $λ_1,\ldots,λ_n$ such that $f$ is a constant map with value $(2λ_1,\cdots,2λ_n)$. We also show each self--map on Khalimsky circle and Khalimsky sphere which has closed graph is a constant map. The text is motivated by examples.

math.GN↗

arXiv2021

On Li--Yorke chaotic transformation groups modulo an ideal

In the following text we introduce the notion of chaoticity modulo an ideal in the sense of Li-Yorke in topological transformation semigroups and bring some of its elementary properties. We continue our study by characterizing a class of abelian infinite Li-Yorke chaotic Fort transformation groups and show all of the elements of the above class is co-decomposable to non-Li-Yorke chaotic transformation groups.

math.DS↗

arXiv2018

Top-designs in the category of Fort spaces

In infinite topological Fort space $X$, for nonempty subsets $C,D$ of $X$ in the following text we answer to this question "Is there any $λ$ and Top--design $C-(X,D,λ)$ of type $i$?" for $i=1,2,3,4$. We prove there exist $λ$ and $C-(X,D,λ)$, Top--design of type 2 (resp. type 4) if and only if $C$ can be embedded into $D$.

math.GN↗