Mathematics

We shall describe tools useful in the study of 3-dimensional flows. The tools are based on partial differential equations of Cauchy-Riemann type. Their solutions allow the construction of global surfaces of sections and, as a generalization, of 2-dimensional foliations transversal to the flow in the complement of finitely many distinguished periodic orbits. Such a global system of transversal sections is established for Reeb-flows on the tight 3-sphere. The applications cover Hamiltonian systems on starlike energy surfaces.