IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i2p533-549.html
   My bibliography  Save this article

Nonlinear dynamics in the Einstein–Friedmann equation

Author

Listed:
  • Tanaka, Yosuke
  • Mizuno, Yuji
  • Ohta, Shigetoshi
  • Mori, Keisuke
  • Horiuchi, Tanji

Abstract

We have studied the gravitational field equations on the basis of general relativity and nonlinear dynamics. The space component of the Einstein–Friedmann equation shows the chaotic behaviours in case the following conditions are satisfied:(i)the expanding ratio: h=x˙/x<0,(ii)the curvature: ζ=−1, and(iii)the cosmological constant: λ<κp.

Suggested Citation

  • Tanaka, Yosuke & Mizuno, Yuji & Ohta, Shigetoshi & Mori, Keisuke & Horiuchi, Tanji, 2009. "Nonlinear dynamics in the Einstein–Friedmann equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 533-549.
  • Handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:533-549
    DOI: 10.1016/j.chaos.2008.02.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908000830
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2008.02.027?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., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    2. Tanaka, Yosuke & Mizuno, Yuji & Kado, Tatsuhiko & Zhao, Hua-An, 2007. "Nonlinear dynamics in the relativistic field equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1054-1075.
    3. El Naschie, M.S., 2005. "The two-slit experiment as the foundation of E-infinity of high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 509-514.
    4. Tanaka, Yosuke & Mizuno, Yuzi & Kado, Tatsuhiko, 2005. "Chaotic dynamics in the Friedmann equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 407-422.
    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. Tanaka, Yosuke & Shudo, Takefumi & Yosinaga, Tetsutaro & Kimura, Hiroshi, 2008. "Relativistic field equations and nonlinear dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 941-949.
    2. Tanaka, Yosuke & Nakano, Shingo & Ohta, Shigetoshi & Mori, Keisuke & Horiuchi, Tanji, 2009. "Einstein–Friedmann equation, nonlinear dynamics and chaotic behaviours," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2159-2173.
    3. Tanaka, Yosuke & Mizuno, Yuji & Kado, Tatsuhiko & Zhao, Hua-An, 2007. "Nonlinear dynamics in the relativistic field equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1054-1075.
    4. Sun, Lei & Cheng, Zhengxing & Huang, Yongdong, 2007. "Construction of trivariate biorthogonal compactly supported wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1412-1420.
    5. Yang, Ciann-Dong, 2007. "The origin and proof of quantization axiom p→pˆ=-iℏ∇ in complex spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 274-283.
    6. Khastan, A. & Ivaz, K., 2009. "Numerical solution of fuzzy differential equations by Nyström method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 859-868.
    7. Saadati, Reza, 2008. "Notes to the paper “Fixed points in intuitionistic fuzzy metric spaces” and its generalization to L-fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 176-180.
    8. Sun, Lei & Zhang, Xiaozhong, 2009. "A note on biorthogonality of the scaling functions with arbitrary matrix dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 711-715.
    9. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    10. 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.
    11. Gregori, V. & Romaguera, S. & Veeramani, P., 2006. "A note on intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 902-905.
    12. Liu, Zhanwei & Hu, Guoen & Lu, Zhibo, 2009. "Parseval frame scaling sets and MSF Parseval frame wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1966-1974.
    13. EL-Nabulsi, Ahmad Rami, 2009. "Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 52-61.
    14. 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.
    15. 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.
    16. Saadati, R. & Sedghi, S. & Shobe, N., 2008. "Modified intuitionistic fuzzy metric spaces and some fixed point theorems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 36-47.
    17. Miheţ, Dorel, 2009. "A note on a fixed point theorem in Menger probabilistic quasi-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2349-2352.
    18. Yang, Ciann-Dong, 2009. "Complex spin and anti-spin dynamics: A generalization of de Broglie–Bohm theory to complex space," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 317-333.
    19. Sun, Lei & Li, Gang, 2009. "Generalized orthogonal multiwavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2420-2424.
    20. Caldas, Miguel & Jafari, Saeid, 2009. "A new decomposition of β-open functions," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 10-12.

    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:41:y:2009:i:2:p:533-549. 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.