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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
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    References listed on IDEAS

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    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. Tanaka, Yosuke & Mizuno, Yuzi & Kado, Tatsuhiko, 2005. "Chaotic dynamics in the Friedmann equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 407-422.
    4. 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.
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