2025/01/16 by Anshid Aboobacker, Aboobacker, Anshid, Gopal, Sharan
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2501.09295
In this paper, we define and study the notions of k-type proximal pairs, k-type asymptotic pairs and k-type Li Yorke sensitivity for dynamical systems given by ℤd actions on compact metric spaces. We prove the Auslander-Yorke dichotomy theorem for k-type notions. The preservation of some of these notions under uniform conjugacy is also studied. We also study relations between these notions and their analogous notions in the usual dynamical systems.