Liouville's theorem for pedants

Recently I've been brushing up on some basic physics for a little side project.

Last Sunday it was time for me to remind myself about the content of Liouville's theorem. Although there are a great many accounts of this important result, I failed to find one that satisfied my differential geometer's tastes. Since it took me several hours to understand this simple result in the way that I wanted, I decided to do my future self a favour and type up some notes. I thought there would be no harm making them available on the web. Here are links to: