2024/07/10 by Shital H. Joshi, Joshi, Shital H., Ekta Shah +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2407.07549
openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the concept of stronger forms of positively expansive map and name it as p \mathscrF-expansive maps. Here \mathscrF is a family of subsets of ℕ. Examples of positively thick expansive and positively syndetic expansive maps are constructed here. Also, we obtain conditions under which a positively expansive map is positively co--finite expansive and positively syndetic expansive maps. Further, we study several properties of p \mathscrF-expansive maps. A characterization of p \mathscrF-expansive maps in terms of p \mathscrF^*-generator is obtained. Here p \mathscrF^* is dual of \mathscrF. Considering (ℤ,+) as a semigroup, we study \mathscrF-expansive homeomorphism, where \mathscrF is a family of subsets of ℤ ∖ \0\. We show that there does not exists an expansive homeomorphism on a compact metric space which is \mathscrFs-expansive. Also, we study relation between \mathscrF-expansivity of f and the shift map σf on the inverse limit space.