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Doctoral Thesis
DOI
10.11606/T.55.2014.tde-29092014-155847
Document
Author
Full name
Giuliano Angelo Zugliani
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2014
Supervisor
Committee
Bergamasco, Adalberto Panobianco (President)
Cordaro, Paulo Domingos
Hounie, Jorge Guillermo
Silva, Paulo Leandro Dattori da
Title in English
Global solvability of systems on compact surfaces
Keywords in English
Complex vector fields
Global solvability
Involutive systems
Abstract in English
We are interested in studying an involutive system defined by a closed non-exact 1-form on a closed and orientable surface. Here we present a necessary condition for the global solvability of this system. We also make some particular constructions of globally solvable systems that motivate the equivalence between the global solvability and the necessary condition, for two cases involving 1-forms of the Morse type, namely, when the surface is the bitorus or when the 1-form is generic
Title in Portuguese
Resolubilidade global de sistemas em superfícies compactas
Keywords in Portuguese
Campos vetoriais complexos
Resolubilidade global
Sistemas involutivos
Abstract in Portuguese
Nosso interesse é estudar um sistema involutivo definido por uma 1-forma fechada e não-exata em uma superfície fechada e orientável. Apresentamos aqui uma condição necessária para a resolubilidade global desde sistema. Nós também construímos exemplos de sistemas globalmente resolúveis que nos permitiram fornecer a equivalência entre a resolubilidade global e a condição necessária, para dois casos envolvendo 1-formas do tipo Morse: quando a superfície é o bitoro ou quando a 1-forma é genérica
 
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Tese_Giuliano.pdf (2.00 Mbytes)
Publishing Date
2014-09-29
 
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