Shadowing properties and chaotic properties of non-autonomous product systems
This paper examines how properties such as shadowing properties, transitivity, and accessibility in non-autonomous discrete dynamical systems carry over to their product systems. The paper establishes a proof that the product system exhibits the pseudo-orbit shadowing property (PSP) if, and only if,...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231021?viewType=HTML |
| _version_ | 1797788548156358656 |
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| author | Jingmin Pi Tianxiu Lu Jie Zhou |
| author_facet | Jingmin Pi Tianxiu Lu Jie Zhou |
| author_sort | Jingmin Pi |
| collection | DOAJ |
| description | This paper examines how properties such as shadowing properties, transitivity, and accessibility in non-autonomous discrete dynamical systems carry over to their product systems. The paper establishes a proof that the product system exhibits the pseudo-orbit shadowing property (PSP) if, and only if, both factor systems possess PSP. This relationship, which is both sufficient and necessary, also holds for the average shadowing property (ASP) and accessibility. Consequently, in practical problem scenarios, certain chaotic properties of two-dimensional systems can be simplified to those observed in one-dimensional systems. However, it should be noted that while the point-transitivity, transitivity, or mixing of the product system can be deduced from the factor systems, the reverse is not true. In particular, this paper constructs counterexamples to demonstrate that some of the theorems presented herein do not hold when considering their inverses. |
| first_indexed | 2024-03-13T01:38:05Z |
| format | Article |
| id | doaj.art-b4e8397a50794a3eb47e78cd9f2534c5 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T01:38:05Z |
| publishDate | 2023-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-b4e8397a50794a3eb47e78cd9f2534c52023-07-04T01:20:22ZengAIMS PressAIMS Mathematics2473-69882023-06-0189200482006210.3934/math.20231021Shadowing properties and chaotic properties of non-autonomous product systemsJingmin Pi 0Tianxiu Lu 1Jie Zhou21. College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, China 2. South Sichuan Applied Mathematics Research Center, Zigong, 643000, China1. College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, China1. College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, ChinaThis paper examines how properties such as shadowing properties, transitivity, and accessibility in non-autonomous discrete dynamical systems carry over to their product systems. The paper establishes a proof that the product system exhibits the pseudo-orbit shadowing property (PSP) if, and only if, both factor systems possess PSP. This relationship, which is both sufficient and necessary, also holds for the average shadowing property (ASP) and accessibility. Consequently, in practical problem scenarios, certain chaotic properties of two-dimensional systems can be simplified to those observed in one-dimensional systems. However, it should be noted that while the point-transitivity, transitivity, or mixing of the product system can be deduced from the factor systems, the reverse is not true. In particular, this paper constructs counterexamples to demonstrate that some of the theorems presented herein do not hold when considering their inverses.https://www.aimspress.com/article/doi/10.3934/math.20231021?viewType=HTMLnon-autonomous discrete dynamical systemsproduct mapshadowing propertiestransitivityaccessibility |
| spellingShingle | Jingmin Pi Tianxiu Lu Jie Zhou Shadowing properties and chaotic properties of non-autonomous product systems AIMS Mathematics non-autonomous discrete dynamical systems product map shadowing properties transitivity accessibility |
| title | Shadowing properties and chaotic properties of non-autonomous product systems |
| title_full | Shadowing properties and chaotic properties of non-autonomous product systems |
| title_fullStr | Shadowing properties and chaotic properties of non-autonomous product systems |
| title_full_unstemmed | Shadowing properties and chaotic properties of non-autonomous product systems |
| title_short | Shadowing properties and chaotic properties of non-autonomous product systems |
| title_sort | shadowing properties and chaotic properties of non autonomous product systems |
| topic | non-autonomous discrete dynamical systems product map shadowing properties transitivity accessibility |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231021?viewType=HTML |
| work_keys_str_mv | AT jingminpi shadowingpropertiesandchaoticpropertiesofnonautonomousproductsystems AT tianxiulu shadowingpropertiesandchaoticpropertiesofnonautonomousproductsystems AT jiezhou shadowingpropertiesandchaoticpropertiesofnonautonomousproductsystems |