We study pseudoholomorphic maps from a punctured Riemann surface into the symplectization of a contact manifold. A Fredholm theory yields the virtual dimension of the moduli spaces of such maps in terms of the Euler characteristic of the Riemann surface and the asymptotics data given by the periodic solutions of the Reeb vector field associated to the contact form. The transversality results establish the existence of additional structure for these spaces. To be more precise, we prove that these spaces are generically smooth manifolds, and therefore their virtual dimension coincides with their actual dimension.

Abstract. In this paper we study a generalized symplectic fixed point problem, first considered by J. Moser in [19], from the point of view of some relatively recently discovered symplectic rigidity phenomena. This problem has interesting applications concerning global perturbations of Hamiltonian systems.

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