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- W2066568163 abstract "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 δm of the interval of a, where the 2m-cycle is stable, to the interval where the 2m+1-cycle is stable scales as δm ≃γ(−1)m/3 (ac γ2/3) 2m, where ac 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 2m-cycle to ac is extremely rapid, and the Feigenbaum constant δ≡lim m →∞ δm 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." @default.
- W2066568163 created "2016-06-24" @default.
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- W2066568163 date "1998-07-01" @default.
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- W2066568163 title "On the Bifurcation of Trapezoid Maps: An Example of a Class of One-Dimensional Maps with a Superconvergent Period Doubling Cascade" @default.
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- W2066568163 doi "https://doi.org/10.1143/ptp.100.39" @default.
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