On special representations of automorphisms of \(\sigma\)-finite measure spaces using Poincaré recurrence theorem and Hopf decomposition (Q6086426)

It is well known that Poincaré's recurrence theorem holds for the measure spaces with finite measure. The authors study when this theorem holds in the more general class of infinite \(\sigma\)-finite measure spaces and, along the way, to discuss and present a constructive proof of Hopf decomposition theorem, as well as to extend and strengthen earlier results.