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Relativistic field equations and nonlinear dynamics

Author

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  • Tanaka, Yosuke
  • Shudo, Takefumi
  • Yosinaga, Tetsutaro
  • Kimura, Hiroshi

Abstract

We have studied the gravitational field equations on the basis of general relativity and nonlinear dynamics. By integrating the space component of the Einstein–Friedmann equation, we have derived the Higgs-type W-shape potential [U=(1/4)(λ−κp)x2−(1/8)ζx4], and classified the solutions in the Einstein–Friedmann equation. We have shown that there occurs 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 & Shudo, Takefumi & Yosinaga, Tetsutaro & Kimura, Hiroshi, 2008. "Relativistic field equations and nonlinear dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 941-949.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:4:p:941-949
    DOI: 10.1016/j.chaos.2008.01.004
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Tanaka, Yosuke & Mizuno, Yuzi & Kado, Tatsuhiko, 2005. "Chaotic dynamics in the Friedmann equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 407-422.
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    1. 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.

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