DEFINING CHAOS IN THE LOGISTIC MAP BY SHARKOVSKII'S THEOREM

被引：1

作者：

Lee, M. Howard ^{[1
,2
]}

机构：

[1] Univ Georgia, Dept Phys & Astron, Athens, GA 30602 USA

[2] Korea Inst Adv Study, Seoul 130012, South Korea

来源：

ACTA PHYSICA POLONICA B | 2013年 / 44卷 / 05期

关键词：

D O I：

10.5506/APhysPolB.44.925

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The fixed points of 3-cycle in the logistic map are obtained by solving a sextic polynomial analytically. Therewith, the domain of chaos is established by Sharkovskii's theorem. A fix-point spectrum is then constructed in the chaotic domain. By Sharkovskii's theorem, a chaotic trajectory is shown to be a superposition of all finite cycles, termed an aleph cycle. An aleph cycle means chaos and it defines chaos in the logistic map in an absolute sense. In particular, a trajectory which is ergodic is aleph-cyclic, hence it is also chaotic.

引用

页码：925 / 935

页数：11

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