Timeline for Can a (non-measurable) autonomous flow have a non-trivial periodic orbit without a minimal period?

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Oct 13, 2015 at 16:42	comment	added	Julian Newman		Thank you very much for this! I now realise that in general, for any periodic point $x \in X$ of the dynamical system $(f^t)$, the dynamics of $(f^t)$ on the set $\{f^t(x):t > 0\}$ are conjugate to the unit-speed translation in the group $\mathbb{R}/G_x$, where $G_x:=\{0\} \cup \{t \in \mathbb{R} \setminus \{0\} : f^{\|t\|}(x)=x\}$. So then, your proof for part II is essentially a proof that for every proper subgroup $G$ of $\mathbb{R}$, $\mathbb{R}/G$ is infinite.
Oct 12, 2015 at 20:56	vote	accept	Julian Newman
Oct 12, 2015 at 20:38	history	edited	Arnaud Chéritat	CC BY-SA 3.0	adding proof of second claim
Oct 12, 2015 at 19:33	history	edited	Arnaud Chéritat	CC BY-SA 3.0	Correcting claim about the finite case.
Oct 12, 2015 at 18:53	history	edited	Arnaud Chéritat	CC BY-SA 3.0	added 127 characters in body
Oct 12, 2015 at 18:30	history	answered	Arnaud Chéritat	CC BY-SA 3.0