06/09/2016, 15:00 — 15:40 — Amphitheatre Pa2, Mathematics Building
Pedro Salomão, IME, Universidade de São Paulo

Systems of transversal sections for Reeb flows on $\mathbb{R}P^3 \# \mathbb{R}P^3$

Global surfaces of section for three-dimensional flows allows one to study dynamics via the first return map. When such global surfaces of section do not exist, it is still possible to consider the so called systems of transversal sections: a transversal foliation to the vector field in the complement of a finite set of periodic orbits. Such systems may provide interesting information about the underlying dynamics. In this talk, I will introduce the notion of systems of transversal sections for Reeb flows on the connected sums of real projective three spaces. In particular, I will present sufficient conditions so that a set formed by three periodic orbits admits a system of transversal section in its complement.

This result is motivated by the restricted three body problem for energies slightly above the first Lagrange value. This is joint work with N. de Paulo (UFSC) and U. Hryniewicz (UFRJ).