Unstable periodic orbits and the symbolic dynamics of the complex Hénon map.
Unstable periodic orbits and the symbolic dynamics of the complex Hénon map.
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DOI：
10.1103/physreva.42.4639
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发表时间：
1990-10
期刊：
影响因子：
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通讯作者：
O. Biham;Wolfgang Wenzel
中科院分区：
文献类型：
--
作者：
O. Biham;Wolfgang Wenzel
提出了一种计算复平面中混沌映射不稳定周期轨道的数值技术。将此技术应用于复 Henon 映射，我们表明它可以找到任意给定阶数 {ital p} 的 2{sup {ital p}} 实数和复数周期轨道。真实的周期轨道与我们之前提出的普通Henon图通过类似算法得到的周期轨道是一致的，从而验证了其完整性。该方法为 Henon 映射提供了符号动力学的新定义，该定义适用于实周期轨道和复周期轨道。它提供了一个计算框架，在一个共同的基础上适用于该图的所有限制，这与传统技术不同，在传统技术中，需要不同的算法来计算涉及奇异吸引子、奇异排斥子和各种类型的 Julia 集。
A numerical technique for the calculation of unstable periodic orbits of chaotic maps in the complex plane is presented. Applying this technique to the complex Henon map we show that it can find {ital all} the 2{sup {ital p}} real and complex periodic orbits of any given order {ital p}. The real periodic orbits coincide with those obtained by a similar algorithm for the ordinary Henon map that we have proposed earlier, and thus verify its completeness. The method provides a new definition of symbolic dynamics for the Henon map, which holds for both the real and complex periodic orbits. It provides a computational framework that applies to all limits of this map on a common footing, unlike the conventional techniques in which one needs different algorithms for calculations involving strange attractors, strange repellers, and various types of Julia sets.