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arXiv · 1607.06165

On $\mathbb{P}$-Weakly Hyperbolic Iterated Function Systems

Ítalo Melo
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Abstract

In this paper we will consider the concept of $\mathbb{P}$-weakly hyperbolic iterated function systems on compact metric spaces that generalizes the concept of weakly hyperbolic iterated function systems, as defined by Edalat in \cite{E} and by Arbieto, Santiago and Junqueira in \cite{ASJ} 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 $\mathbb{P}$-weakly hyperbolic IFS. Furthermore, we prove an ergodic theorem for $\mathbb{P}$-weakly hyperbolic IFS with compact parameter space.

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Ítalo Melo. 2016-07-21. On $\mathbb{P}$-Weakly Hyperbolic Iterated Function Systems. https://arxiv.org/abs/1607.06165

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