Irrational contact ellipsoid flow on the three-sphere
= Irrational contact ellipsoid flow on the three-sphere
For $\alpha_s=\frac12(r_1^2d\theta_1+sr_2^2d\theta_2)$ on $S^3$, the Reeb field is $2\partial_{\theta_1}+2s^{-1}\partial_{\theta_2}$. If $s$ is irrational, its only closed orbits are the two coordinate circles.