Work

Shadowing Properties and Chaotic Characteristics in Time-varying Discrete Dynamical Systems

Year: 2025

Type: article

Abstract: Let $ f_{1,\infty} $ be a map sequence on a compact metric space $ (X,d) $. First, this paper defines $ NK $-th iteration map sequence $ f_{1,\infty}^{n[k]} $, where $ f_{1,\infty}^{n[k]}=\{f^{nk}_{\frac{n(n-1)k}{2}+1}\}_{n=1}^{\infty} $ $ (k\in \mathbb{N}) $. It is proved that $ f_{1,\infty} $ is $ \mathcal{P} $-chaotic (or has pseudo-orbit shadowing property) if and only if $ f_{1,\infty}^{n[k]} $ is also $ \mathcal{P} $-chaotic (or has pseudo-orbit shadowing property). Where $ \mathcal{P} $-chaos denotes one of the nine properties: Li-Yorke chaos, distributional chaotic, dense chaos, dense $ \delta $-chaos, generic chaos, generic $ \delta $-chaos, Li-Yorke sensitivity, sensitivity, spatio-temporal chaos. Then, the preservation of persistence, expansive, linking, topological stability, and six types of shadowing properties in time-varying discrete dynamical systems (T-VDDSs) under product operator or topological conjugacy are shown. Moreover, a homeomorphism that is expansive and has the eventual shadowing property necessarily implies topological stability.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20250023

Authors: Jiazheng Zhao, Tianxiu Lu, Yue Zhang

Institution: Sichuan University of Science and Engineering

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Sichuan University of Science and Engineering, Sichuan University, Natural Science Foundation of Sichuan Province

Award: G3349664061