IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v332y2004icp219-229.html
   My bibliography  Save this article

Periodic orbits and chaotic-diffusion probability distributions

Author

Listed:
  • Dana, Itzhack
  • Chernov, Vladislav E

Abstract

Periodic-orbit (PO) formulas for chaotic-diffusion probability distributions (PDs) are examined in the case of the perturbed Arnol'd cat map on the cylinder. This translationally invariant system exhibits a transition from uniform to nonuniform hyperbolicity as the perturbation parameter is increased. Two coarse-grained PDs, describing the “diffusion” between unit cells of the system, are studied: (a) a PD based on PO ensembles; (b) a PD based on generic ensembles. The approximate PO formula for PD (b) gives results which fluctuate around the expected Gaussian distribution for all parameters considered and thus agree qualitatively with results from standard methods. The exact PO formula for PD (a) gives similar results only for sufficiently small parameters. The results for large parameters decrease monotonically relative to the Gaussian distribution. This deviation seems to disappear as the PO period is increased.

Suggested Citation

  • Dana, Itzhack & Chernov, Vladislav E, 2004. "Periodic orbits and chaotic-diffusion probability distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 219-229.
    • Handle: RePEc:eee:phsmap:v:332:y:2004:i:c:p:219-229
    DOI: 10.1016/j.physa.2003.10.050
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437103009531
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2003.10.050?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.

    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:phsmap:v:332:y:2004:i:c:p:219-229. 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.

    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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.