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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

1 vote
0 answers
95 views

Generalizing an application of the Poincaré-Bendixson theorem

I was looking for applications of the Poincaré-Bendixson theorem and on this site I have found several examples almost all similar to this post. So I tried to make a quite natural generalization $$ \l …
Zaragosa's user avatar
  • 143
3 votes
0 answers
198 views

The best applications of the Poincaré-Bendixson theorem [closed]

I'm reading about the Poincaré-Bendixson theorem in the plane, I really liked the theorem. I have seen common applications in Sotomayor and Perko's book. But I would like to know what other applicatio …
Zaragosa's user avatar
  • 143
7 votes
2 answers
407 views

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 …
Zaragosa's user avatar
  • 143