Cyclic stabilisators for the coadjoint representation of the group of diffeomorphisms of the circle (Q1972900)

The author studies the regular coadjoint orbits of the group \(\text{Diff}^+(S^1)\) of the diffeomorphisms of the circle that are isotopic to the identity. It is shown that the stabilizer of the quadratic differential \(u(x)(\text{d} u)^2\) is cyclic if and only if the set of zeros of the function \(u\) is nonempty and its interior is empty. A sufficient condition for the triviality of this stabilizer is also given.