IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v54y2013icp122-126.html
   My bibliography  Save this article

Irregular recurrence in compact metric spaces

Author

Listed:
  • Obadalová, Lenka

Abstract

For a continuous map f:X→X of a compact metric space, the set IR(f) of irregularly recurrent points is the set of points which are upper density recurrent, but not lower density recurrent. These notions are related to the structure of the measure center, but many problems still remain open. We solve some of them. The main result, based on examples by Obadalová and Smítal [Obadalová L, Smítal J. Counterexamples to the open problem by Zhou and Feng on minimal center of attraction. Nonlinearity 2012;25:1443–9], shows that positive topological entropy supported by the center Cz of attraction of a point z is not related to the property that Cz is the support of an invariant measure generated by z. We also show that IR(f) is invariant with respect to standard operations, like f(IR(f))=IR(f), or IR(fm)=IR(f) for m∈N.

Suggested Citation

  • Obadalová, Lenka, 2013. "Irregular recurrence in compact metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 122-126.
    • Handle: RePEc:eee:chsofr:v:54:y:2013:i:c:p:122-126
    DOI: 10.1016/j.chaos.2013.06.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077913001240
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2013.06.010?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:54:y:2013:i:c:p:122-126. 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.