Timeline for How to prove Liouville measure is invariant under geodesic flow?

10 events

when toggle format	what		by	license	comment
Nov 12, 2017 at 9:12	history	edited	Ivan Izmestiev	CC BY-SA 3.0	added 2 characters in body
Dec 9, 2015 at 9:18	answer	added	Matthias Ludewig		timeline score: 11
Dec 8, 2015 at 13:12	answer	added	Mikhail Katz		timeline score: 4
Dec 8, 2015 at 13:09	history	edited	oneyear	CC BY-SA 3.0	edited title
Dec 8, 2015 at 13:07	comment	added	oneyear		@SebastianGoette: Thank you for your comments, I correct my mistake. I have read several textbooks on Riemannian geometry, but I have not find this theorem. So can you show where I can find a direct proof? Or can you give one?
Dec 8, 2015 at 13:01	history	edited	oneyear	CC BY-SA 3.0	deleted 72 characters in body
Dec 8, 2015 at 11:40	review	Close votes
Dec 10, 2015 at 17:46
Dec 8, 2015 at 11:22	comment	added	Sebastian Goette		For $y\in SM$ let $\gamma_y(t)=\exp(ty)\in M$ be the unique geodesic with initial velocity $y$. Then $\Phi_t(y)=\dot\gamma_y(t)\in SM$ defines the geodesic flow. In particular, both $\Omega\subset SM$ and $\Phi_t(\Omega)\subset SM$. You should find a proof of the invariance of the Liouville measure in any good textbook on Riemannian geometry.
Dec 8, 2015 at 11:07	comment	added	user1688		The measure lives on the sphere bundle, the flow acts on the sphere bundle, so the meaning of invariance should be clear.
Dec 8, 2015 at 9:21	history	asked	oneyear	CC BY-SA 3.0