IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v145y1987i3p425-460.html
   My bibliography  Save this article

Period doubling in maps with a maximum of order z

Author

Listed:
  • Van Der Weele, J.P.
  • Capel, H.W.
  • Kluiving, R.

Abstract

We consider the scaling behaviour in period-doubling systems, exemplified by the one-dimensional map χn+1 = 1 − λ|χn|z, which has a maximum of order z (z > 1). The Feigenbaum scaling factors α and δ are studied as functions of z, and more generally the scaling functions 1/σ and ƒ(a). In particular, using the universal functions g(x) and h(x) we establish the inequality δ < αz, which implies that δ remains finite (≲ 30) in the limit z → ∞.

Suggested Citation

  • Van Der Weele, J.P. & Capel, H.W. & Kluiving, R., 1987. "Period doubling in maps with a maximum of order z," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 145(3), pages 425-460.
  • Handle: RePEc:eee:phsmap:v:145:y:1987:i:3:p:425-460
    DOI: 10.1016/0378-4371(87)90004-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437187900045
    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/10.1016/0378-4371(87)90004-5?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. Skogan, Wesley G., 1982. "Police and Community in Japan. By Walter L. Ames. (Berkeley: University of California Press, 1981. Pp. xvi + 245. $22.50.)," American Political Science Review, Cambridge University Press, vol. 76(3), pages 679-680, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Van Der Weele, J.P. & Capel, H.W., 1987. "The ƒ(a) formalism applied to the crossover from conservative to dissipative scaling behaviour in period doubling systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 297-314.
    2. Post, T. & Capel, H.W. & Van der Weele, J.P., 1989. "Phase-length distributions in intermittent band switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(3), pages 321-350.
    3. Post, Thijs & Capel, Hans W., 1991. "Windows in one-dimensional maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(1), pages 62-100.

    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. Post, Thijs & Capel, Hans W., 1991. "Windows in one-dimensional maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(1), pages 62-100.

    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:phsmap:v:145:y:1987:i:3:p:425-460. 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: 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.