IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v39y2009i5p2041-2047.html
   My bibliography  Save this article

Gauss map and Lyapunov exponents of interacting particles in a billiard

Author

Listed:
  • Manchein, C.
  • Beims, M.W.

Abstract

We show that the Lyapunov exponent (LE) of periodic orbits with Lebesgue measure zero from the Gauss map can be used to determine the main qualitative behavior of the LE of a Hamiltonian system. The Hamiltonian system is a one-dimensional box with two particles interacting via a Yukawa potential and does not possess Kolmogorov–Arnold–Moser (KAM) curves. In our case the Gauss map is applied to the mass ratio (γ=m2/m1) between particles. Besides the main qualitative behavior, some unexpected peaks in the γ dependence of the mean LE and the appearance of ‘stickness’ in phase space can also be understand via LE from the Gauss map. This shows a nice example of the relation between the “instability” of the continued fraction representation of a number with the stability of non-periodic curves (no KAM curves) from the physical model. Our results also confirm the intuition that pseudo-integrable systems with more complicated invariant surfaces of the flow (higher genus) should be more unstable under perturbation.

Suggested Citation

  • Manchein, C. & Beims, M.W., 2009. "Gauss map and Lyapunov exponents of interacting particles in a billiard," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2041-2047.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2041-2047
    DOI: 10.1016/j.chaos.2007.06.112
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790700447X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.06.112?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.

    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:39:y:2009:i:5:p:2041-2047. 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.