IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2011y2011i1n520273.html

Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space

Author

Listed:
  • Qiuju Xing
  • Yuming Shi

Abstract

This paper is concerned with distribution of maps with transversal homoclinic orbits in a continuous map space, which consists of continuous maps defined in a closed and bounded set of a Banach space. By the transversal homoclinic theorem, it is shown that the map space contains a dense set of maps that have transversal homoclinic orbits and are chaotic in the sense of both Li‐Yorke and Devaney with positive topological entropy.

Suggested Citation

  • Qiuju Xing & Yuming Shi, 2011. "Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:520273
    DOI: 10.1155/2011/520273
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2011/520273
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/520273?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
    ---><---

    References listed on IDEAS

    as
    1. Jacob Palis Jr. & Welington de Melo, 1982. "Geometric Theory of Dynamical Systems," Springer Books, Springer, number 978-1-4612-5703-5, October.
    2. Shi, Yuming & Ju, Hyonhui & Chen, Guanrong, 2009. "Coupled-expanding maps and one-sided symbolic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2138-2149.
    Full references (including those not matched with items on IDEAS)

    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. Yingying Zeng, 2014. "Local Cr Stability for Iterative Roots of Orientation‐Preserving Self‐Mappings on the Interval," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Kim, Cholsan & Ju, Hyonhui & Chen, Minghao & Raith, Peter, 2015. "A-coupled-expanding and distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 291-295.
    3. Kim, Jinhyon & Ju, Hyonhui, 2018. "Hausdorff dimension of the sets of Li-Yorke pairs for some chaotic dynamical systems including A-coupled expanding systems," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 246-251.
    4. Ju, Hyonhui & Kim, Cholsan & Choe, Yunmi & Chen, Minghao, 2017. "Conditions for topologically semi-conjugacy of the induced systems to the subshift of finite type," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 1-6.

    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:wly:jnlaaa:v:2011:y:2011:i:1:n:520273. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.