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Dynamics, topology and holomorphic curves. (English) Zbl 0908.58020

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).

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
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