IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1602-d415003.html
   My bibliography  Save this article

Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori

Author

Listed:
  • Jan Andres

    (Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic)

  • Jerzy Jezierski

    (Department of Informatics and Mathematics, Warsaw University of Life Sciences, Nowoursynowska 159, 02 757 Warsaw, Poland)

Abstract

The main aim of this article is two-fold: (i) to generalize into a multivalued setting the classical Ivanov theorem about the lower estimate of a topological entropy in terms of the asymptotic Nielsen numbers, and (ii) to apply the related inequality for admissible pairs to impulsive differential equations and inclusions on tori. In case of a positive topological entropy, the obtained result can be regarded as a nontrivial contribution to deterministic chaos for multivalued impulsive dynamics.

Suggested Citation

  • Jan Andres & Jerzy Jezierski, 2020. "Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori," Mathematics, MDPI, vol. 8(9), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1602-:d:415003
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1602/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1602/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andres, Jan, 2020. "Chaos for multivalued maps and induced hyperspace maps," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    Full references (including those not matched with items on IDEAS)

    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.
    1. Andres, Jan & Ludvík, Pavel, 2022. "Topological entropy of multivalued maps in topological spaces and hyperspaces," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

    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:8:y:2020:i:9:p:1602-:d:415003. 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.