IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v105y2017icp224-229.html
   My bibliography  Save this article

Quasi-Lipschitz mapping, correlation and local dimensions

Author

Listed:
  • Yang, Jiaojiao
  • Wu, Min
  • Zhang, Yiwei

Abstract

In this article, we discuss two important and related concepts in the studies of geometric dimension theory, e.g. the correlation dimension and the local dimension of measures. Our results can be summarized as the following two aspects: on one hand, we show that the correlation dimension of measures is invariant under the quasi-Lipschitz mapping, and also give a sufficient condition for the coincidence of the correlation dimension and the Hausdorff dimension of measures. On the other hand, we examine the local dimensions in the limit sets of Moran construction in abstract metric space, with reasonably weaker separation condition. These discussions generalized several known results by Mattila, Moran and Rey in [14] and Li, Lou and Wu in [10,11].

Suggested Citation

  • Yang, Jiaojiao & Wu, Min & Zhang, Yiwei, 2017. "Quasi-Lipschitz mapping, correlation and local dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 224-229.
    • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:224-229
    DOI: 10.1016/j.chaos.2017.10.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791730454X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.10.037?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. Wu, Min & Xiao, JiaQing, 2011. "The singularity spectrum of some non-regularity moran fractals," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 548-557.
    2. Yang, Jiaojiao & Käenmäki, Antti & Wu, Min, 2017. "A note on correlation and local dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 39-43.
    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. Khelifi, Mounir & Lotfi, Hela & Samti, Amal & Selmi, Bilel, 2020. "A relative multifractal analysis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Achour, Rim & Li, Zhiming & Selmi, Bilel & Wang, Tingting, 2024. "A multifractal formalism for new general fractal measures," Chaos, Solitons & Fractals, Elsevier, vol. 181(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:105:y:2017:i:c:p:224-229. 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.