IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v207y2026ics0960077926001384.html

Limit cycles of planar discontinuous piecewise linear Hamiltonian systems in three regions of Y-type

Author

Listed:
  • Llibre, Jaume
  • Oliveira, Regilene

Abstract

In recent years there has been a significant interest in studying discontinuous piecewise differential systems, mainly due to the wide range of applications in modeling natural phenomena. To understand the dynamics of these systems in the plane one challenge is to control their number of limit cycles. In this paper we study the existence of limit cycles in planar discontinuous piecewise linear Hamiltonian systems with three zones separated by the line Y={(x,y):x≥0andy=0}∪{(x,y):x=0andy≥0}∪{(x,y):x≤0andy=0}. We provide the maximum number of crossing limit cycles intersecting each branch of Y in one point, and intersecting two branches of the Y each one in two points. So we have solved the extension of the 16th Hilbert problem to this class of differential systems.

Suggested Citation

  • Llibre, Jaume & Oliveira, Regilene, 2026. "Limit cycles of planar discontinuous piecewise linear Hamiltonian systems in three regions of Y-type," Chaos, Solitons & Fractals, Elsevier, vol. 207(C).
    • Handle: RePEc:eee:chsofr:v:207:y:2026:i:c:s0960077926001384
    DOI: 10.1016/j.chaos.2026.117997
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077926001384
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2026.117997?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;

    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:207:y:2026:i:c:s0960077926001384. 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.