3-2-1 foliations for Reeb flows on S³

• Autor(a) principal: Oliveira, Carolina Lemos de
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-28042020-160658/
• topic: Curvas pseudo-holomorfas; Dinâmica Hamiltoniana; Finite energy foliations; Fluxos de Reeb; Folheações de energia finita; Hamiltonian dynamics; Pseudoholomorphic curves; Reeb Flows

In this work, we study global systems of transverse sections for Reeb flows associated with tight contact forms on the 3-sphere. These flows include, in particular, Hamiltonian flows on R^4 restricted to star-shaped regular energy levels. A global system of transverse sections naturally generalizes the concept of global surface of section. It is a singular foliation of S³ whose singular set consists of finitely many periodic orbits, called binding orbits, and the regular leaves are transverse to the flow. The aim of this work is to use the theory of pseudoholomorphic curves in symplectizations to study the existence of a particular type of system of transverse sections, called 3-2-1 foliation, which has exactly three binding orbits with Conley-Zehnder indices respectively 3, 2 and 1. More precisely, we give sufficient conditions under which three Reeb orbits are the binding orbits of a 3-2-1 foliation.