IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v166y2023ics0960077922010694.html
   My bibliography  Save this article

Point-extended box dimension

Author

Listed:
  • Maaroufi, Nadir
  • Zerouali, El Hassan

Abstract

11We would like to extend our thanks to the College of Engineering and Architecture of the International University of Rabat for supporting this project through one-year teaching discharge granted to professor Maaroufi Nadir to finalize the drafting of this article. This article is mainly concerned by the concept of dimension. More precisely, our objective is to challenge the conventional zero dimension assigned to the point. This reconsideration allows us to propose two new ways of conceiving the notion of dimension, which are the two sides of the same coin. First, the dimension of a set appears as a quantification of the organization of its points. Secondly, the dimension seems essentially to be a comparison between the entropies of sets. Thus, we started from the point and succeeded in constructing a point-dimension notion allowing us to extend the principle of box dimension in many directions and to finely estimate the dimensions of sets. More precisely, we introduce the notion of point-extended box dimension in the large framework of topological vector spaces, freeing it from the notion of metric. This general setting permits us to treat the case of finite, infinite and invisible dimensions. This first work focuses essentially on general properties and is particularly oriented towards establishing a well founded framework for infinite dimension.

Suggested Citation

  • Maaroufi, Nadir & Zerouali, El Hassan, 2023. "Point-extended box dimension," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010694
    DOI: 10.1016/j.chaos.2022.112890
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922010694
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112890?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Yanguang, 2020. "Equivalent relation between normalized spatial entropy and fractal dimension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    2. Maaroufi, Nadir, 2016. "Invariance and computation of the extended fractal dimension for the attractor of CGL on R," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 87-96.
    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. Yanqi Zhao & Yue Zhang & Ying Yang & Fan Li & Rongkun Dai & Jianlin Li & Mingshi Wang & Zhenhua Li, 2023. "The Impact of Land Use Structure Change on Utilization Performance in Henan Province, China," IJERPH, MDPI, vol. 20(5), pages 1-18, February.
    2. Răzvan-Cornel Sfetcu & Vasile Preda, 2023. "Fractal Divergences of Generalized Jacobi Polynomials," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    3. Ortiz-Vilchis, Pilar & Lei, Mingli & Ramirez-Arellano, Aldo, 2024. "Reformulation of Deng information dimension of complex networks based on a sigmoid asymptote," Chaos, Solitons & Fractals, Elsevier, vol. 180(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:eee:chsofr:v:166:y:2023:i:c:s0960077922010694. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.