IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v31y2020i12ns0129183120501740.html
   My bibliography  Save this article

Preperiodicity and systematic extraction of periodic orbits of the quadratic map

Author

Listed:
  • Jason A. C. Gallas

    (Instituto de Altos Estudos da Paraíba, Rua Silvino Lopes 419-2502, 58039-190 João Pessoa, Brazil2Complexity Sciences Center, 9225 Collins Ave. Suite 1208, Surfside FL 33154, USA3Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany)

Abstract

Iteration of the quadratic map produces sequences of polynomials whose degrees explode as the orbital period grows more and more. The polynomial mixing all 335 period-12 orbits has degree 4020, while for the 52 377 period-20 orbits the degree rises already to 1 047 540. Here, we show how to use preperiodic points to systematically extract exact equations of motion, one by one, without any need for iteration. Exact orbital equations provide valuable insight about the arithmetic structure and nesting properties of towers of algebraic numbers which define orbital points and bifurcation cascades of the map.

Suggested Citation

  • Jason A. C. Gallas, 2020. "Preperiodicity and systematic extraction of periodic orbits of the quadratic map," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(12), pages 1-13, December.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:12:n:s0129183120501740
    DOI: 10.1142/S0129183120501740
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183120501740
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183120501740?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:wsi:ijmpcx:v:31:y:2020:i:12:n:s0129183120501740. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    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.