Systems of transversal sections for 3-dimensional Reeb flows

• Grant number: 17/07330-7
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2017
• End date: June 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Pedro Antonio Santoro Salomão
• Grantee: Pedro Antonio Santoro Salomão
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Since the works of Poincaré and Birkhoff global cross sections are used to study Hamiltonian dynamics restricted to energy levels. Modern methods in Sympletic Dynamics provide an alternative way to study dynamics when such cross sections do not exist. The so called systems of transversal sections are codimension 1 singular foliations of the energy level whose singularity is formed by finitely many periodic orbits. Such systems are obtained via pseudo holomorphic curves in the symplectization of contact manifolds. This projects focus on the existence of the systems of transversal sections for classical Hamiltonian systems such as the Euler problem in the plane and the restricted three body problem. (AU)