k-type Chaos for Induced Group Actions on Hyperspaces

2025/11/20 by Anshid Aboobacker, Aboobacker, Anshid
Computer Science · Mathematics · #37B05 #37C85 #54B20 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2511.16841

openalex publication_date 2025/11/20 · openalex created_date 2025/11/25 · openalex updated_date 2026/08/04

Abstract

This paper investigates the correlation between k-type dynamical properties of ℤ^d-actions on compact metric spaces and their induced actions on the corresponding hyperspaces. We extend the classical results from discrete dynamical systems and general group actions to the specific setting of k-type dynamics. Specifically, we define and study k-type transitivity, k-type mixing, k-type weak mixing, and k-type Li-Yorke chaos for induced hyperspace actions, establishing that these properties transfer from the base system to the hyperspace under appropriate conditions.

Related

• Chaotic behavior of group actions
• On definition of Devaney chaos for a continuous group action on a Hausdorff uniform space
• Induced Dynamics in Hyperspaces of Non-Autonomous Discrete Systems
• Induced Dynamics of Non-Autonomous Discrete Dynamical Systems
• On generic and dense chaos for maps induced on hyperspaces