Superconvergence of Period-Doubling Cascade in Trapezoid Maps : Its Rigorous Proof and Superconvergence of the Period-Doubling Cascade Starting from a Period p Solution

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概要

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• In the symmetric and the asymmetric trapezoid maps, as a slope a of the trapezoid is increased, a period-doubling cascade occurs.The symbolic sequence of periodic points in this cascade is the Metropolis-Stein-Stein sequence R~*m, and the convergence of the onset points a_m of the period 2~m solutions to the accumulation point a_c is exponentially fast.In a previous paper, we proved these results.In this paper, we give a detailed description of proofs regarding the results.Further, we study the period-doubling cascade starting from the period p(≥3) solution and show that the convergence of the onset points of the period p×2~m solutions is also exponentially fast.

• 一般社団法人日本物理学会の論文
• 2000-07-25

著者

• Uezu Tatsuya

  Graduate School Of Human Culture Nara Women's University

• UEZU Tatsuya

  Graduate School of Human Culture, Nara Women's University

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