IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v36y2008i3p532-538.html
   My bibliography  Save this article

The Hausdorff and box-counting dimensions of a class of recurrent sets

Author

Listed:
  • Dai, Meifeng
  • Liu, Xi

Abstract

It is well known that a lot of familiar fractal sets can be generated using recurrent method. Conclusions under similitude linear map are straightforward. In this paper, we study the upper and low bounds for the Hausdorff dimension and boxing-counting dimension of recurrent sets. Especially, we focus our attention on the case of the non-similitude.

Suggested Citation

  • Dai, Meifeng & Liu, Xi, 2008. "The Hausdorff and box-counting dimensions of a class of recurrent sets," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 532-538.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:3:p:532-538
    DOI: 10.1016/j.chaos.2006.06.083
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906006837
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.06.083?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.

    References listed on IDEAS

    as
    1. Naschie, M.S. El, 2006. "Fractal black holes and information," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 23-35.
    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. El Naschie, M.S., 2006. "On two new fuzzy Kähler manifolds, Klein modular space and ’t Hooft holographic principles," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 876-881.
    2. Yin, Xin-An & Yang, Xiao-Hua & Yang, Zhi-Feng, 2009. "Using the R/S method to determine the periodicity of time series," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 731-745.
    3. Chen, Ning & Hao, Ding & Tang, Ming, 2009. "Automatic generation of symmetric IFSs contracted in the hyperbolic plane," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 829-842.
    4. Chen, Qing-Jiang & Qu, Xiao-Gang, 2009. "Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1676-1683.
    5. Altun, Ishak & Sahin, Hakan & Aslantas, Mustafa, 2021. "A new approach to fractals via best proximity point," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Zhang, Yongping & Sun, Weihua & Liu, Shutang, 2009. "Control of generalized Julia sets," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1738-1744.
    7. Chiou, Juing-Shian & Cheng, Chun-Ming, 2009. "Stabilization analysis of the switched discrete-time systems using Lyapunov stability theorem and genetic algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 751-759.
    8. Singh, S.L. & Prasad, Bhagwati & Kumar, Ashish, 2009. "Fractals via iterated functions and multifunctions," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1224-1231.
    9. Singh, S.L. & Jain, Sarika & Mishra, S.N., 2009. "A new approach to superfractals," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3110-3120.
    10. Nozari, Kourosh & Mehdipour, S. Hamid, 2009. "Failure of standard thermodynamics in planck scale black hole system," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 956-970.
    11. Gottlieb, I. & Agop, M., 2007. "El Naschie’s ε(∞) theory and an alternative to gauged spacetime scale relativity theory," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1025-1029.
    12. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and characterizations of orthogonal vector-valued multivariate wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1835-1844.
    13. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    14. Agop, M. & Enache, V., 2007. "Gauge theories on El Naschie’s ε(∞) space-time topology," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 296-301.
    15. El Naschie, Mohamed Saladin, 2006. "Is gravity less fundamental than elementary particles theory? Critical remarks on holography and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 803-807.
    16. Llorens-Fuster, Enrique & Petruşel, Adrian & Yao, Jen-Chih, 2009. "Iterated function systems and well-posedness," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1561-1568.
    17. El Naschie, M.S., 2008. "High energy physics and the standard model from the exceptional Lie groups," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 1-17.
    18. Naschie, M.S. El, 2006. "Holographic correspondence and quantum gravity in E-infinity spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 871-875.
    19. Sidharth, B.G., 2006. "Strings and Planck oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 300-311.
    20. Zheng, Jing & Lin, Zhengyan & Tong, Changqing, 2009. "The Hausdorff dimension of the range for the Markov processes of Ornstein–Uhlenbeck type," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2008-2013.

    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:36:y:2008:i:3:p:532-538. 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: 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.