IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v139y2020ics096007792030583x.html
   My bibliography  Save this article

Realization of a snowflaked interval as a Euclidean self-similar set

Author

Listed:
  • Koparal, Fatma Diğdem
  • Özdemir, Yunus
  • Çelik, Derya
  • Koçak, Şahin

Abstract

The metric space ([0, 1], dα) with 0 < α < 1 is called a snowflaked version of the interval [0,1] with the standard metric d. Assouad has shown in 1983 that such a snowflaked interval can be embedded bi-Lipschitzly into RNwhere N=[[1α]]+1. We give an alternative proof of this nice theorem in terms of iterated function systems (IFS). We construct three similitudes on RNsuch that the image of the snowflaked interval under our bi-Lipschitz embedding becomes the attractor of the IFS consisting of these three similitudes. In this way the image of the bi-Lipschitz embedding becomes a self-similar subset of RNwith Hausdorff dimension 1α.

Suggested Citation

  • Koparal, Fatma Diğdem & Özdemir, Yunus & Çelik, Derya & Koçak, Şahin, 2020. "Realization of a snowflaked interval as a Euclidean self-similar set," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s096007792030583x
    DOI: 10.1016/j.chaos.2020.110187
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792030583X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110187?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.

    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:139:y:2020:i:c:s096007792030583x. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.