IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i6p1384-d1095571.html
   My bibliography  Save this article

The Ergodicity and Sensitivity of Nonautonomous Discrete Dynamical Systems

Author

Listed:
  • Risong Li

    (School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China)

  • Tianxiu Lu

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

  • Hongqing Wang

    (School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China)

  • Jie Zhou

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

  • Xianfeng Ding

    (School of Science, Southwest Petroleum University, Chengdu 610500, China)

  • Yongjiang Li

    (School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China)

Abstract

Let ( E , h 1 , ∞ ) be a nonautonomous discrete dynamical system (briefly, N.D.D.S.) that is defined by a sequence ( h j ) j = 1 ∞ of continuous maps h j : E → E over a nontrivial metric space ( E , d ) . This paper defines and discusses some forms of ergodicity and sensitivity for the system ( E , h 1 , ∞ ) by upper density, lower density, density, and a sequence of positive integers. Under some conditions, if the rate of convergence at which ( h j ) j = 1 ∞ converges to the limit map h is “fast enough” with respect to a sequence of positive integers with a density of one, it is shown that several sensitivity properties for the N.D.D.S. ( E , h 1 , ∞ ) are the same as those properties of the system ( E , h ) . Some sufficient conditions for the N.D.D.S. ( E , h 1 , ∞ ) to have stronger sensitivity properties are also presented. The conditions in our results are less restrictive than those in some existing works, and the conclusions of all the theorems in this paper improve upon those of previous studies. Thus, these results are extensions of the existing ones.

Suggested Citation

  • Risong Li & Tianxiu Lu & Hongqing Wang & Jie Zhou & Xianfeng Ding & Yongjiang Li, 2023. "The Ergodicity and Sensitivity of Nonautonomous Discrete Dynamical Systems," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1384-:d:1095571
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/6/1384/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/6/1384/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Huoyun Wang & Jincheng Xiong & Feng Tan, 2010. "Furstenberg Families and Sensitivity," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-12, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Imran Nasim & Michael E. Henderson, 2024. "Dynamically Meaningful Latent Representations of Dynamical Systems," Mathematics, MDPI, vol. 12(3), pages 1-14, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1384-:d:1095571. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.