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1. CMB 2004 (vol 47 pp. 607)

Plamenevskaya, Olga
 A Residue Formula for $\SU(2)$-Valued Moment Maps Jeffrey and Kirwan gave expressions for intersection pairings on the reduced space $M_0=\mu^{-1}(0)/G$ of a Hamiltonian $G$-space $M$ in terms of multiple residues. In this paper we prove a residue formula for symplectic volumes of reduced spaces of a quasi-Hamiltonian $\SU(2)$-space. The definition of quasi-Hamiltonian $G$-spaces was recently introduced in . Category:58F05

2. CMB 2001 (vol 44 pp. 323)

Schuman, Bertrand
 Une classe d'hamiltoniens polynomiaux isochrones Soit $H_0 = \frac{x^2+y^2}{2}$ un hamiltonien isochrone du plan $\Rset^2$. On met en \'evidence une classe d'hamiltoniens isochrones qui sont des perturbations polynomiales de $H_0$. On obtient alors une condition n\'ecessaire d'isochronisme, et un crit\ere de choix pour les hamiltoniens isochrones. On voit ce r\'esultat comme \'etant une g\'en\'eralisation du caract\ere isochrone des perturbations hamiltoniennes homog\`enes consid\'er\'ees dans [L], [P], [S]. Let $H_0 = \frac{x^2+y^2}{2}$ be an isochronous Hamiltonian of the plane $\Rset^2$. We obtain a necessary condition for a system to be isochronous. We can think of this result as a generalization of the isochronous behaviour of the homogeneous polynomial perturbation of the Hamiltonian $H_0$ considered in [L], [P], [S]. Keywords:Hamiltonian system, normal forms, resonance, linearizationCategories:34C20, 58F05, 58F22, 58F30

3. CMB 2001 (vol 44 pp. 129)

Currás-Bosch, Carlos
 LinÃ©arisation symplectique en dimension 2 In this paper the germ of neighborhood of a compact leaf in a Lagrangian foliation is symplectically classified when the compact leaf is $\bT^2$, the affine structure induced by the Lagrangian foliation on the leaf is complete, and the holonomy of $\bT^2$ in the foliation linearizes. The germ of neighborhood is classified by a function, depending on one transverse coordinate, this function is related to the affine structure of the nearly compact leaves. Keywords:symplectic manifold, Lagrangian foliation, affine connectionCategories:53C12, 58F05
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