Invariant measures on multi-valued functions

In this paper we consider the question of under which conditions multi-valued dynamical systems admit invariant measures. We give results on the existence of invariant measures with full support on orbit spaces of multi-valued dynamical systems. We use these measures on the orbit space to induce mea...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2017-12, Vol.456 (1), p.616-627
Main Authors: Meddaugh, Jonathan, Raines, Brian E., Tennant, Tim
Format: Article
Language:English
Subjects:
Invariant measure
Inverse limit
Multi-valued function
Specification property
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Summary:In this paper we consider the question of under which conditions multi-valued dynamical systems admit invariant measures. We give results on the existence of invariant measures with full support on orbit spaces of multi-valued dynamical systems. We use these measures on the orbit space to induce measures on the original dynamical system. We focus on the question of when a non-atomic invariant measure on the orbit space induces an atomic invariant measure on the multi-valued dynamical system. This phenomenon is an indicator of complicated multi-periodic behaviour.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.07.009