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

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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 (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 \(\mathbb {P}\)-weakly hyperbolic IFS. Furthermore, we prove an ergodic theorem for \(\mathbb {P}\)-weakly hyperbolic IFS with compact parameter space.

Keywords

Iterated function systems Invariant measure Ergodic theorem 
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Notes

Acknowledgements

The author would like to thank to Ermerson Araujo and Fernando Lenarduzzi for useful conversations during the preparation of this work. The author was supported by a CNPq-Brazil doctoral fellowship.

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Copyright information

© Sociedade Brasileira de Matemática 2017

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal do PiauíTeresinaBrazil

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