IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v28y2006i2p377-385.html
   My bibliography  Save this article

Smale horseshoe via the anti-integrability

Author

Listed:
  • Chen, Yi-Chiuan

Abstract

The embedding of the Bernoulli shift into the horseshoe map can be viewed as it is inherited from the anti-integrable limit where the horseshoe has infinite contraction in one direction and infinite expansion in the other. At the limit the map is virtually a subshift of finite type with four symbols or equivalently a full shift with two symbols. We present an algebraic explanation for the equivalence of the two shifts.

Suggested Citation

  • Chen, Yi-Chiuan, 2006. "Smale horseshoe via the anti-integrability," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 377-385.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:2:p:377-385
    DOI: 10.1016/j.chaos.2005.05.050
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790500545X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.05.050?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuan, Quan & Li, Qingdu & Yang, Xiao-Song, 2009. "Horseshoe chaos in a class of simple Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1522-1529.

    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:eee:chsofr:v:28:y:2006:i:2:p:377-385. 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.