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Einstein–Friedmann equation, nonlinear dynamics and chaotic behaviours

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  • Tanaka, Yosuke
  • Nakano, Shingo
  • Ohta, Shigetoshi
  • Mori, Keisuke
  • Horiuchi, Tanji

Abstract

We have studied the Einstein–Friedmann equation [Case 1] on the basis of the bifurcation theory and shown that the chaotic behaviours in the Einstein–Friedmann equation [Case 1] are reduced to the pitchfork bifurcation and the homoclinic bifurcation. We have obtained the following results:

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2159-2173
    DOI: 10.1016/j.chaos.2009.03.205
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    References listed on IDEAS

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    1. Tanaka, Yosuke, 2007. "The mass spectrum of heavier hadrons and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 996-1007.
    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, 2009. "Space–time symmetry violation, configuration mixing model and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1064-1072.
    4. Tanaka, Yosuke & Mizuno, Yuzi & Kado, Tatsuhiko, 2005. "Chaotic dynamics in the Friedmann equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 407-422.
    5. 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.
    6. Tanaka, Yosuke, 2006. "The mass spectrum of hadrons and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 851-863.
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