IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v237y1997i3p387-404.html
   My bibliography  Save this article

Nonintegrability, chaos, and complexity

Author

Listed:
  • McCauley, Joseph L.

Abstract

Two-dimensional driven-dissipative flows are generally integrable via a conservation law that is singular at equilibria. Nonintegrable dynamical systems are confined to n⩾3 dimensions. Even driven-dissipative deterministic dynamical systems that are critical, chaotic or complex have n − 1 local time-independent conservation laws that can be used to simplify the geometric picture of the flow over as many consecutive time intervals as one likes. Those conservation laws generally have either branch cuts, phase singularities, or both. The consequence of the existence of singular conservation laws for experimental data analysis, and also for the search for scale-invariant critical states via uncontrolled approximations in deterministic dynamical systems, is discussed. Finally, the expectation of ubiquity of scaling laws and universality classes in dynamics is contrasted with the possibility that the most interesting dynamics in nature may be nonscaling, nonuniversal, and to some degree computationally complex.

Suggested Citation

  • McCauley, Joseph L., 1997. "Nonintegrability, chaos, and complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(3), pages 387-404.
    • Handle: RePEc:eee:phsmap:v:237:y:1997:i:3:p:387-404
    DOI: 10.1016/S0378-4371(96)00408-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437196004086
    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/S0378-4371(96)00408-6?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. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N., 2012. "Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma, Part one: Sunspot dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6287-6319.

    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:237:y:1997:i:3:p:387-404. 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.