IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v30y2006i2p374-379.html
   My bibliography  Save this article

Fractal dimension of chaotic dynamical spaces

Author

Listed:
  • Nada, S.I.

Abstract

In his paper [Chaos, Solitons & Fractals 4 (1994) 293–6], E1 Naschie has exposed the existence of sets with dimensions between 0 and −1, which he calls the cantorian sets. E1-Ghoul discussed some problems in fractal dimensions [Chaos, Solitons & Fractals, England 4 (2001) 77–80; Chaos, Solitons & Fractals, England 18 (2003) 187–92]. The present work is intended to extend their works for chaotic dynamical manifolds. This is obviously related to the cantorian geometry with a possible model for quantum mechanics. The folding of these spaces and their relations with dimensions are studied. Special emphasis on ε-dimension, 0<ε≪1 is given and some generalized theorems from classical dimension theory are introduced.

Suggested Citation

  • Nada, S.I., 2006. "Fractal dimension of chaotic dynamical spaces," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 374-379.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:2:p:374-379
    DOI: 10.1016/j.chaos.2005.09.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905009057
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.09.039?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. El Naschie, M.S., 2005. "From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 969-977.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nada, S.I. & Zohny, H., 2009. "An application of relative topology in biology," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 202-204.

    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. Khastan, A. & Ivaz, K., 2009. "Numerical solution of fuzzy differential equations by Nyström method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 859-868.
    2. Sadeqi, I. & Kia, F. Solaty, 2009. "Fuzzy normed linear space and its topological structure," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2576-2589.
    3. Agop, M. & Murgulet, C., 2007. "Ball lightning as a self-organizing process of a plasma–plasma interface and El Naschie’s ε(∞) space–time," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 754-769.
    4. Agop, M. & Rusu, Ioana, 2007. "El Naschie’s self-organization of the patterns in a plasma discharge: Experimental and theoretical results," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 172-186.
    5. El Naschie, Mohamed Saladin, 2006. "The idealized quantum two-slit gedanken experiment revisited—Criticism and reinterpretation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 843-849.
    6. Dehghan, Mehdi & Hashemi, Behnam & Ghatee, Mehdi, 2007. "Solution of the fully fuzzy linear systems using iterative techniques," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 316-336.
    7. Chalco-Cano, Y. & Román-Flores, H., 2008. "On new solutions of fuzzy differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 112-119.
    8. Soleimani-damaneh, M., 2009. "Establishing the existence of a distance-based upper bound for a fuzzy DEA model using duality," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 485-490.
    9. Sahin, Bayram, 2008. "Screen transversal lightlike submanifolds of indefinite Kaehler manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1439-1448.
    10. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    11. Qiu, Dong & Shu, Lan & Guan, Jian, 2009. "Common fixed point theorems for fuzzy mappings under Φ-contraction condition," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 360-367.
    12. Agop, M. & Craciun, P., 2006. "El Naschie’s Cantorian gravity and Einstein’s quantum gravity," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 30-40.
    13. Abu-Donia, H.M., 2007. "Common fixed point theorems for fuzzy mappings in metric space under ϕ-contraction condition," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 538-543.
    14. Soleimani-damaneh, M., 2009. "Maximal flow in possibilistic networks," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 370-375.
    15. Azab Abd-Allah, M. & El-Saady, Kamal & Ghareeb, A., 2009. "Rough intuitionistic fuzzy subgroup," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2145-2153.
    16. Deshpande, Bhavana, 2009. "Fixed point and (DS)-weak commutativity condition in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2722-2728.
    17. Farnoosh, R. & Aghajani, A. & Azhdari, P., 2009. "Contraction theorems in fuzzy metric space," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 854-858.
    18. Agop, M. & Craciun, P., 2006. "El Naschie’s ε(∞) space–time and the two slit experiment in the Weyl–Dirac theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 441-452.
    19. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
    20. Soleimani-damaneh, M., 2008. "Fuzzy upper bounds and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 217-225.

    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:30:y:2006:i:2:p:374-379. 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.