On Weakly Hyperbolic Iterated Function Systems
On Weakly Hyperbolic Iterated Function Systems
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DOI：
10.1007/s00574-016-0018-4
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发表时间：
2012-11
期刊：
影响因子：
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通讯作者：
A. Arbieto;André Junqueira;B. Santiago
中科院分区：
文献类型：
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作者：
A. Arbieto;André Junqueira;B. Santiago
我们研究了紧度量空间上的弱双曲迭代函数系统，如Edalat（Inform Comput 124（2）：182-197，1996）所定义的，但在更一般的紧参数空间中。从拓扑和测度理论的观点以及不变测度的遍历性证明了吸引子的存在性。在完备度量空间和紧参数空间中定义了弱双曲迭代函数系，推广了上述定义。此外，我们还研究了在这种情况下吸引子的存在性问题。最后，我们证明了Barnsley和Vince（Ergodic Theory Dyn Syst 31（4）：1073-1079，2011）关于在紧参数空间中绘制吸引子（所谓的混沌博弈）的结果。
We study weakly hyperbolic iterated function systems on compact metric spaces, as defined by Edalat (Inform Comput 124(2):182–197, 1996), but in the more general setting of compact parameter space. We prove the existence of attractors, both in the topological and measure theoretical viewpoint and the ergodicity of invariant measure. We also define weakly hyperbolic iterated function systems for complete metric spaces and compact parameter space, extending the above mentioned definition. Furthermore, we study the question of existence of attractors in this setting. Finally, we prove a version of the results by Barnsley and Vince (Ergodic Theory Dyn Syst 31(4):1073–1079, 2011), about drawing the attractor (the so-called the chaos game), for compact parameter space.