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Mar 15, 2018 at 1:48 vote accept Adam
Mar 14, 2018 at 14:12 comment added Lee Mosher Because if $\mathcal{F}^u_\phi$ were transverse to $\mathcal{F}$ then a long leaf segment of $\mathcal{F}^u_\phi$ which intersects every leaf of $\mathcal{F}$ could be approximated by a closed curve transverse to and intersecting every leaf of $\mathcal F$, which directly violates the property of transverse recurrence.
Mar 14, 2018 at 14:03 comment added Adam Many thanks for this very comprehensive answer! A quick follow-up: Why $\cal F$ being not trasversely recurrent implies that no $\cal F_\phi^u$ is transversal to $\cal F$?
Mar 7, 2018 at 16:41 history edited Lee Mosher CC BY-SA 3.0
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Mar 7, 2018 at 16:10 history answered Lee Mosher CC BY-SA 3.0