This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in (4). We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic… Expand

Surfaces of sections are a classical tool in the study of 3-dimensional dynamical systems. Their use goes back to the work of Poincare and Birkhoff. In the present paper we give a natural… Expand

We study pseudoholomorphic maps ~ u = (a; u): _ S ! R M de-ned on punctured Riemannian surfaces, satisfying T ~ u i = ~ J T ~ u, with a special almost complex structure ~ J associated with a contact… Expand

Abstract.This is the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. In general, these spaces are not locally homeomorphic to open… Expand

This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. These spaces, in general, are locally not homeomorphic to open sets in… Expand

\widetilde{J}-holomorphic cylinders in \mathbb{R}\times M, where M is a contact manifold are investigated. It is shown that a sufficiently long cylinder having small area is close to a constant map,… Expand