In this paper we define infinite weakly hyperbolic iterated function systems associated with uniformly Dini continuous weight functions. We study the Ruelle operator theorem for the infinite weakly hyperbolic iterated function systems associated with uniformly Dini continuous weight functions. We prove the existence and uniqueness of the invariant measure for these type systems.

中文翻译：

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无限弱双曲迭代函数系统的不变测度

在本文中，我们定义了与均匀 Dini 连续权函数相关的无限弱双曲迭代函数系统。我们研究了与均匀 Dini 连续权函数相关的无限弱双曲迭代函数系统的 Ruelle 算子定理。我们证明了这些类型系统的不变测度的存在性和唯一性。