IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v292y2019i5p1032-1042.html
   My bibliography  Save this article

On the Lipschitz equivalence of self‐affine sets

Author

Listed:
  • Jun Jason Luo

Abstract

Recently Lipschitz equivalence of self‐similar sets on Rd has been studied extensively in the literature. However for self‐affine sets the problem is more awkward and there are very few results. In this paper, we introduce a w‐Lipschitz equivalence by repacing the Euclidean norm with a pseudo‐norm w. Under the open set condition, we prove that any two totally disconnected integral self‐affine sets with a common matrix are w‐Lipschitz equivalent if and only if their digit sets have equal cardinality. The main methods used are the technique of pseudo‐norm and Gromov hyperbolic graph theory on iterated function systems.

Suggested Citation

  • Jun Jason Luo, 2019. "On the Lipschitz equivalence of self‐affine sets," Mathematische Nachrichten, Wiley Blackwell, vol. 292(5), pages 1032-1042, May.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:5:p:1032-1042
    DOI: 10.1002/mana.201800041
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.201800041
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.201800041?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
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:bla:mathna:v:292:y:2019:i:5:p:1032-1042. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    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.