On the Bifurcation of Trapezoid Maps : An Example of a Class of One-Dimensional Maps with a Superconvergent Period Doubling Cascade : Condensed Matter and Statistical Physics

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概要

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• We investigate the period doubling cascade in symmetric and asymmetric trapezoid maps. We prove that as the slope a of the trapezoid is increased, there occurs a cascade of period doubling bifurcations. Further we prove that the symbolic sequence is the Metropolis-Stein-Stein sequence R^<*m> and that the ratio δ_m of the interval of a, where the 2^m-cycle is stable, to the interval where the 2^<m+1>-cycle is stable scales as δ_m ≃ γ^<(-1)^m/3>(a_cγ^<2/3>)^2^m, where a_c is the accumulation point of the period doubling cascade, and γ is the ratio of the two slopes of the trapezoid. That is, convergence of the onset point of the 2^m -cycle to a_c is extremely rapid, and the Feigenbaum constant δ ≡ lim_<m→∞>δ_m is infinite. Further, we give approximate expressions for the accumulation point as functions of b, the length of the smaller side of the trapezoid. The agreement between theoretical results and numerically obtained data is excellent.

• 理論物理学刊行会の論文
• 1998-07-25

著者

• FUJIWARA Yoshikazu

  Department of Physics, Kyoto University

• FUJIWARA Yoshihisa

  Research Institute for Theoretical Physics, Hiroshima University

• FUJIWARA Yoshikazu

  School of Physics, University of Minnesota

• FUJIWARA Yoshikazu

  Research Institute for Fandamental Physics, Kyoto University

• Uezu Tatsuya

  Department Of Physics Kyoto University

• UEZU Tatsuya

  Graduate School of Human Culture, Nara Women's University

• FUJIWARA Yoshihisa

  Department of Physics, Tokyo Institute of Technology

• FUJIWARA Yoshikazu

  Institute of Theoretical Physics, University of Regensburg : Department of Physics, Kyoto University

• FUJIWARA Yoshikazu

  Research institute for Fundamental Phyisics, Kyoto Universtiy,Fellow of the Japan Society for the Promotion of Science

• Fujiwara Yuka

  Department of Physics,Nara Women's University

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