Symplectic dynamics in dimension 3

Abstract

Recent methods in symplectic topology, such as pseudo-holomorphic curves, constitute one of the most advanced tools for studying conservative dynamics. Several classical problems in dynamics can be attacked using these tools, such as geodesic flows, Hamiltonian dynamics etc. In this project, I plan to keep researching in this new area, called symplectic dynamics, proving results for Reeb dynamics in dimension 3, such as existence and multiplicity of periodic orbits, existence of systems of transversal sections to the flow, dynamical characterizations of contact manifolds, and may other things. (AU)