The G-Asymptotic Tracking Property and G-Asymptotic Average Tracking Property in the Inverse Limit Spaces under Group Action

Abstract

Firstly, we introduce the definitions of G-asymptotic tracking property, G-asymptotic average tracking property, and G-quasi-weak almost-periodic point. Secondly, we study their dynamical properties and characteristics. The results obtained improve the conclusions of asymptotic tracking property, asymptotic average tracking property, and quasi-weak almost-periodic point in the inverse limit space and provide the theoretical basis and scientific foundation for the application of tracking property in computational mathematics, biological mathematics, and computer science.