2025/05/21 by Shital H. Joshi, Joshi, Shital H., Ekta Shah +1
Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2505.15286
openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
We define and study stronger forms of Devaney chaos and name it as \mathscrF-Devaney chaos, where \mathscrF is a family of subsets of ℕ. Examples of maps which is \mathscrFt-Devaney chaotic but not \mathscrFcf-Devaney chaotic, \mathscrFs-Devaney chaotic but neither \mathscrFt-Devaney chaotic nor \mathscrFcf-Devaney chaotic are discussed. Further, we show that for the maps on infinite metric space without isolated points, \mathscrF-sensitivity is a redundant condition in the definition \mathscrF-Devaney chaos. Here \mathscrF=\mathscrFs, \mathscrFt, \mathscrFts or \mathscrFcf. We also obtain conditions under which Devaney chaos implies \mathscrFs-Devaney chaos or \mathscrFt-Devaney chaos. Next, we define the concept of (\mathscrF, \mathscrG)-P-chaos and obtain conditions under which (\mathscrF1, \mathscrG1)-P-chaos implies \mathscrF-Devaney chaos for different families \mathscrF1 and \mathscrG1.