Global solvability for a class of involutive systems

Author(s)

Cléber de Medeira

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2012-03-30

Examining board members

Adalberto Panobianco Bergamasco; Milton da Costa Lopes Filho; Marcos da Silva Montenegro; José Ruidival Soares dos Santos Filho; Paulo Leandro Dattori da Silva

• Advisor: Adalberto Panobianco Bergamasco; Sergio Luis Zani

Abstract

We study the global solvability of a class of involutive systems with n smooth vector fields on the torus of dimension n + 1. We obtain a complete characterization for the uncoupled case of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space. Also, we exhibit a special situation where the system is not globally solvable and we use this to obtain some results in a more general case (AU)