On $$\mathbb {P}$$P-Weakly Hyperbolic Iterated Function Systems
On $$\mathbb {P}$$P-Weakly Hyperbolic Iterated Function Systems
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DOI：
10.1007/s00574-017-0042-z
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
Í. Melo
中科院分区：
文献类型：
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作者：
Í. Melo
在这篇文章中，我们将考虑紧度量空间上的-弱双曲迭代函数组的概念，它推广了Edalat(inf Comput124(2)：182-197,1996)和Arbieto，Santiago和Junqueira(Bull Braz Math Soc New Ser 2016)定义的弱双曲迭代函数组的概念，其中参数空间是紧度量空间。证明了a-弱双曲迭代函数系统的不变测度的存在唯一性。此外，我们还证明了参数空间紧的-弱双曲迭代函数系统的遍历定理。
In this paper we will consider the concept of-weakly hyperbolic iterated function systems on compact metric spaces that generalizes the concept of weakly hyperbolic iterated function systems, as defined by Edalat (Inf Comput 124(2):182–197, 1996) and by Arbieto, Santiago and Junqueira (Bull Braz Math Soc New Ser 2016) for a more general setting where the parameter space is a compact metric space. We prove the existence and uniqueness of the invariant measure of a-weakly hyperbolic IFS. Furthermore, we prove an ergodic theorem for-weakly hyperbolic IFS with compact parameter space.