@article{Ji2022, 
author = {Zhanjiang Ji},
title = {The research of    (            G        ,            w        )-Chaos and G-Lipschitz shadowing property},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {10180-10194},
keywords = {inverse limit space, topological G− conjugate, iterative map, (G, w)−Chaos, G− Lipschitz shadowing property},
url = {https://www.sciopen.com/article/10.3934/math.2022566},
doi = {10.3934/math.2022566},
abstract = {In this paper, we introduce the concepts of    (  G  ,  w  )  − Chaos and    G  − Lipschitz shadowing property. We study the dynamical properties of    (  G  ,  w  )  − Chaos in the inverse limit space under group action. In addition, we study the dynamical properties of    G  − Lipschitz shadowing property respectively under topological    G  − conjugate and iterative systems. The following conclusions are obtained. (1) Let    (            X      f        ,            G      ¯        ,                    d      ¯        ,  σ  ) be the inverse limit space of    (  X  ,  G  ,  d  ,  f  ) under group action. If the self-map    f is    (  G  ,  w  )  − chaotic, the shift map    σ is    (  G  ,  w  )  − chaotic; (2) Let    (  X  ,  d  ) be a metric    G  − space and    f be topologically    G  − conjugate to    g. Then the map    f has    G  − Lipschitz shadowing property if and only if the map    g has    G  − Lipschitz shadowing property. (3) Let    (  X  ,  d  ) be a metric    G  − space and    f be an equivariant Lipschitz map from    X to    X. Then for any positive integer    k  ⩾  2, the map    f has the    G  − Lipschitz shadowing property if and only if the iterative map              f      k       has the    G  − Lipschitz shadowing property. These results enrich the theory of topological    G  − conjugate, iterative system and the inverse limit space under group action.}
}