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Zbl 0853.17022
Guieu, Laurent
Rotation number, geometrical structures on a circle and Bott-Virasoro group. (Nombre de rotation, structures géométriques sur un cercle et groupe de Bott-Virasoro.) (French)
[J] Ann. Inst. Fourier 46, No.4, 971-1010 (1996). ISSN 0373-0956; ISSN 1777-5310/e

Summary: A complete classification of coadjoint stabilizers of the Bott-Virasoro group is obtained via an essentially geometrical method. The basic tool is the rotation number of a diffeomorphism of the circle. In particular, we find non-connected isotropy groups and show that the Miura transformation of Hill's operators can be seen as a moment map on the space of affine structures on the circle.

MSC 2000:: *17B68 Virasoro and related algebras
34A26 Geometric methods in differential equations
53A20 Projective differential geometry
58D27 Moduli problems for diff.geometric structures on spaces of mappings
37E99 Low-dimensional dynamical systems

Keywords: Bott-Virasoro group; coadjoint representation; projective structures; Hill's equation; rotation number

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