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Nov 12, 2017 at 11:17 comment added Mikhail Katz Thanks, @BenMcKay. I haven't thought about this recently and it would take too much time to correct my answer. If you think it is misleading I will delete it. Another possibility would be for you to correct it so as to remove inaccuracies since you seem to be on top of the material currently.
Nov 12, 2017 at 11:14 comment added Ben McKay Arnold's proof is for the symplectic volume form on the cotangent bundle, not the induced volume form on the unit sphere bundle. Note that the volume form on the unit sphere bundle is not an invariant of the contact structure on the unit sphere bundle, so the result is not an immediate consequence of Arnold's proof.
Apr 13, 2017 at 12:58 history edited CommunityBot
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Dec 8, 2015 at 13:24 history edited Mikhail Katz CC BY-SA 3.0
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Dec 8, 2015 at 13:12 history answered Mikhail Katz CC BY-SA 3.0