# Kneser theorem about the Klein bottle

I know that in $$1923$$ H. Kneser showed that a continuous flow in a Klein bottle without singular points has a periodic trajectory. The original article is this, but does anyone know another old or new proof of this result? (So far I have found the article by Kneser, the article by Nelson G. Markley and some works that use the results of these articles, I am looking for some other idea focused on proving the result mentioned at the beginning) I would really like to read this result, I tried to do it from your original article but the language is too complicated for me. I searched on the internet but found almost nothing about the proof. I asked here but I didn't find any answer even with bounty. I hope to have some help it would help me a lot.

• I would imagine it to be a contradiction argument. If there is no closed orbit, you argue that the forward-time flow of a point must be clustering in a thin Moebius band, and the same kind of argument as in Poincare-Bendixson tells you the centre of that Moebius band is a closed orbit. You could probably avoid repeating the Poincare-Bendixson argument by covering the Moebius band with an annulus, which is planar. May 26 at 20:20
• @RyanBudney Thank you very much for the idea, it is interesting I will try it, if you have time you give it more form as an answer and in case I manage to finish it I will write it too. May 26 at 21:28