A stochastic adding machine and complex dynamics.
A stochastic adding machine and complex dynamics.
复制标题
随机加法机和复杂的动力学。
DOI：
10.1088/0951-7715/13/6/302
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发表时间：
2000
期刊：
影响因子：
1.7
通讯作者：
Taylor,ThomasJ
中科院分区：
文献类型：
--
作者：
Killeen,PeterR;Taylor,ThomasJ
本文考虑了自然数上马尔可夫链的属性，该属性对二进制加法机进行了建模，其中每次寄存器尝试递增后续寄存器并重置时，失败的概率都为非零。该链具有自然商马尔可夫链族，并且自然地扩展到 2-adic 整数上的链。这些链的转移算子具有自相似结构，并且具有不同程度的谱，该谱是复平面的二次映射的朱莉娅集或填充朱莉娅集。
This paper considers properties of a Markov chain on the natural numbers which models a binary adding machine in which there is a non-zero probability of failure each time a register attempts to increment the succeeding register and resets. This chain has a family of natural quotient Markov chains, and extends naturally to a chain on the 2-adic integers. The transition operators of these chains have a self-similar structure, and have a spectrum which is, variously, the Julia set or filled Julia set of a quadratic map of the complex plane.