Hofer, Helmut H. W. Dynamics, topology and holomorphic curves. (English) Zbl 0908.58020 Doc. Math., Extra Vol. ICM Berlin 1998, vol. I, 255-280 (1998). The author describes the intimate interplay between certain classes of dynamical systems and a holomorphic curve theory. He emphasizes this interplay in real dimension three. The author gives a tool to construct global surfaces of section and generalizations thereof for the large class of Reeb vector fields, which includes, in particular, all geodesic flows on surfaces. (There are many aspects touching areas like Gromov-Witten invariants, quantum cohomology, symplectic homology, Seiberg-Witten invariants, Hamiltonian dynamics and more). Reviewer: George M.Rassias (Athens) Cited in 7 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53D25 Geodesic flows in symplectic geometry and contact geometry Keywords:Hamiltonian dynamics; contact forms; Reeb vector fields; quantum cohomology; Gromov-Witten invariants; Arnold conjecture; Weinstein conjecture; symplectic homology; surfaces of section PDFBibTeX XMLCite \textit{H. H. W. Hofer}, Doc. Math. Extra Vol., 255--280 (1998; Zbl 0908.58020) Full Text: EMIS