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Invariant measures for random expanding on average Saussol maps

Fawwaz Batayneh

School of Mathematics and Physics, The University of Queensland, Saint Lucia, Queensland 4072, Australia

E-mail Address: f.batayneh@uq.edu.au

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and

Cecilia González-Tokman

School of Mathematics and Physics, The University of Queensland, Saint Lucia, Queensland 4072, Australia

E-mail Address: cecilia.gt@uq.edu.au

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https://doi.org/10.1142/S0219493722500150Cited by:1 (Source: Crossref)

This article is part of the issue:

Special Issue in Memory of María J. Garrido-Atienza
Guest Editor: Tomas Caraballo

Abstract

In this paper, we investigate the existence of random absolutely continuous invariant measures (ACIP) for random expanding on average Saussol maps in higher dimensions. This is done by the establishment of a random Lasota–Yorke inequality for the transfer operators on the space of bounded oscillation. We prove that the number of ergodic skew product ACIPs is finite and will provide an upper bound for the number of these ergodic ACIPs. This work can be seen as a generalization of the work in [F. Batayneh and C. González-Tokman, On the number of invariant measures for random expanding maps in higher dimensions, Discrete Contin. Dyn. Syst. 41 (2021) 5887–5914] on admissible random Jabłoński maps to a more general class of higher-dimensional random maps.

Keywords:

AMSC: 37H15, 37C30

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