On Periodic Orbits of Trapezoid Maps
On Periodic Orbits of Trapezoid Maps
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关于梯形映射的周期轨道
DOI：
10.1006/aama.1993.1010
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
S. Doi
中科院分区：
文献类型：
--
作者：
S. Doi
研究了一类特殊的一维平面分段线性梯形映射的迭代问题。利用符号动力学方法，证明了映射的稳定周期轨道是Sun和Helmberg推广意义下的有限移位极大序列，并确定了映射产生任意周期稳定周期轨道的参数区域.本文所用的方法是将梯形映射的分歧问题转化为帐篷（三角形）映射的初值问题的一种简单方法。该方法适用于具有平坦段的各种混沌映射。
Iterations of a special one-dimensional map (trapezoid map) which is a piecewise linear map with a flat top are studied. Using a symbolic dynamical method, it is shown that the stable periodic orbits of the map are characterized as finite shift maximal sequences in the sense extended by Sun and Helmberg and the parameter regions where the map produces a stable periodic orbit with any period are determined. The method used in the present paper is a simple method which converts a bifurcation problem of trapezoid maps to an initial value problem of a tent (triangle) map. This method is applicable to various chaotic maps which have a flat segment.