A COMPUTATIONAL ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS
A COMPUTATIONAL ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS
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DOI：
10.1142/s0219493708002354
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发表时间：
2008-09
影响因子：
1.1
通讯作者：
N. D. Cong;Doan Thai Son;S. Siegmund
中科院分区：
文献类型：
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作者：
N. D. Cong;Doan Thai Son;S. Siegmund
迭代函数系统是随机动力系统的例子，并且作为分形的生成器而流行，如Sierpinski垫圈和Barnsley蕨类。本文证明了由可数多个函数组成的迭代函数系统在任意紧化度量空间上的一个遍历定理，并给出了这个遍历定理在欧几里德空间上的一个计算版本，它允许数值逼近时间平均值和一个显式误差界。结果应用于一个显式算例。
Iterated function systems are examples of random dynamical systems and became popular as generators of fractals like the Sierpinski Gasket and the Barnsley Fern. In this paper we prove an ergodic theorem for iterated function systems which consist of countably many functions and which are contractive on average on an arbitrary compact metric space and we provide a computational version of this ergodic theorem in Euclidean space which allows to numerically approximate the time average together with an explicit error bound. The results are applied to an explicit example.