[This is a follow-up to my question Is there a Möbius torus?]
- There are five clear-cut families of geodesics.
- Most of the geodesics are "chaotic": aperiodic and covering either the entire surface - by spiraling endlessly around the torus - or substantial parts of it.
- Some of the geodesics are "boring": the meridians, the inner and the outer equator
- A few of them are "æsthetically pleasing": returning to their starting point after just a few circuits around the z axis
What I tried to ask in my previous question:
Can the structure of geodesics on the torus change drastically when twisting the "hose" before gluing its ends?
For example: There might be no equator anymore because after twisting the (two) equators lost their "ends".
[I also posted this question at MO.]