Period doubling bifurcations for families of maps on ℝn
Period doubling bifurcations for families of maps on ℝn
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ℝn 上映射族的倍周期分岔
DOI：
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发表时间：
1981
期刊：
影响因子：
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通讯作者：
H. Koch
中科院分区：
文献类型：
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作者：
P. Collet;J. Eckmann;H. Koch
单参数映射族(1-PF)中的无限倍周期分叉序列具有很强的普适性：这在许多情况下都是数值已知的，并且对于区间上的某些1-PF映射族已被严格地证明。这些分支出现在解析映射的1-PF中，当参数的值趋于一个极限时，渐近几何比为1/4.6692…本文给出了证明从ℂn到ℂn的解析映射的1-PF也是如此的主要步骤，其对ℝn的限制是实的。
Infinite sequences of period doubling bifurcations in one-parameter families (1-pf) of maps enjoy very strong universality properties: This is known numerically in a multitude of cases and has been shown rigorously for certain 1-pf of maps on the interval. These bifurcations occur in 1-pf of analytic maps at values of the parameter tending to a limit with the asymptotically geometric ratio 1 /4.6692 ....In this paper we indicate the main steps of a proof that the same is true for 1-pf of analytic maps from ℂn to ℂn, whose restriction to ℝn is real.