Oct. 12, 2023, 14.00-16.00, 233B, International Center for Mathematics.

Title: Transverse foliations for unbounded contact-type energy surfaces in R^4

Speaker: Pedro Salomão.

Abstract: A transverse foliation adapted to a three-dimensional flow consists of a finite set of periodic orbits, called binding orbits, and a smooth foliation of its complement by properly embedded surfaces that are transverse to the flow. Transverse foliations generalize open book decompositions and are used to find periodic orbits, homoclinics and heteroclinics to hyperbolic orbits, etc. I will introduce some conditions for a Reeb flow to admit a transverse foliation with prescribed binding orbits, and present an application to the spatial isosceles three-body problem for unbounded energy surfaces. This is work in progress with Liu Lei (Shandong University).