IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4419-9058-7_12.html
   My bibliography  Save this book chapter

Dynamics and Bifurcation Near the Transition from Stability to Complex Instability

In: New Advances in Celestial Mechanics and Hamiltonian Systems

Author

Listed:
  • M. Ollé

    (ETSEIB (UPC), Dept. de Matemàtica Aplicada I)

  • J. R. Pacha

    (ETSEIB (UPC), Dept. de Matemàtica Aplicada I)

  • J. Villanueva

    (ETSEIB (UPC), Dept. de Matemàtica Aplicada I)

Abstract

We consider a Hamiltonian of three degrees of freedom and a family of periodic orbits with a transition from stability to complex instability, such that there is an irrational collision of the Floquet multipliers of opposite sign. We analyze the local dynamics and the bifurcation phenomena linked to this transition. We study the resulting Hamiltonian Hopf-like bifurcation from an analytical point of view by means of normal forms. The existence of a bifurcating family of 2D tori is derived and both cases (direct and inverse bifurcation) are described.

Suggested Citation

  • M. Ollé & J. R. Pacha & J. Villanueva, 2004. "Dynamics and Bifurcation Near the Transition from Stability to Complex Instability," Springer Books, in: J. Delgado & E. A. Lacomba & J. Llibre & E. Pérez-Chavela (ed.), New Advances in Celestial Mechanics and Hamiltonian Systems, pages 185-197, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-9058-7_12
    DOI: 10.1007/978-1-4419-9058-7_12
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    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:spr:sprchp:978-1-4419-9058-7_12. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.