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Symmetric measure-preserving systems. (English) Zbl 0942.28016

Summary: A symmetric measure-preserving system is one where the measure \(\mu\) is preserved by two maps \(T\) and \(R\) where \(R\) is self-inverse and \(T\circ R = T\). We discuss the existence of such systems and some consequences, including when unimodal maps are conjugate to the symmetric tent map.

MSC:

28D05 Measure-preserving transformations
47A35 Ergodic theory of linear operators
37A05 Dynamical aspects of measure-preserving transformations
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