STABLE ORBITS AND BIFURCATION OF MAPS OF INTERVAL
STABLE ORBITS AND BIFURCATION OF MAPS OF INTERVAL
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DOI：
10.1137/0135020
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发表时间：
1978-01-01
影响因子：
1.9
通讯作者：
SINGER, D
中科院分区：
文献类型：
--
作者：
SINGER, D
在处处负Schwarzian导数的假设下，证明了至少从单位区间到自身的类的可微映射有有限个稳定的周期轨道，每个周期轨道吸引某个临界点的迭代.一个例子说明了这一假设的必要性，它表明具有一个临界点的单位区间的自同态可以拥有多个稳定轨道。
Differentiable maps of class at leastfrom the unit interval to itself are shown to have a finite number of stable periodic orbits, each of which attracts the iterates of some critical point, assuming the hypothesis of everywhere negative Schwarzian derivative. An example illustrates the necessity of this hypothesis; it shows that an endomorphism of the unit interval with one critical point may possess more than one stable orbit.