Someone knows a book that have the proof of the Poincaré Recurrence Theorem for flows when the set have finite volume and when don't?
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2$\begingroup$ Apart from the initial papers of Poincare and the subsequent version of the proof by Caratheodory (you can find these references for example in: encyclopediaofmath.org/wiki/Poincar%C3%A9_return_theorem), i think you can find a proof for the ergodic "version" of the theorem at: P. Walters, An introduction to ergodic theory, Graduate Texts in Mathematics, Vol. 79. 1982. $\endgroup$– Konstantinos KanakoglouCommented Jul 27, 2020 at 2:55
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