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Semiglobal solvability for classes of non-singular vector fields

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Author(s):
Vinícius Novelli da Silva
Total Authors: 1
Document type: Master's Dissertation
Press: São Carlos.
Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
Defense date:
Examining board members:
Paulo Leandro Dattori da Silva; Alexandre Kirilov; Gerson Petronilho; Sergio Luis Zani
Advisor: Paulo Leandro Dattori da Silva
Abstract

In this work, we study a family of first-order partial differential operators defined in a neighborhood of an invariant torus Tm0 : = Tm x ⊂ Tm x Rn. These operators have orbits (in the sense of Sussmann) which are contained in Tm0. We prove that, if a certain diophantine condition (of Siegel-type) is satisfied, it is possible to determine a normal form for these operators in a neighborhood of the invariant torus. In this case, we also prove a semiglobal solvability result. We discuss the problem in the C∞ (smooth) and Cω (real-analytic) categories. (AU)

FAPESP's process: 17/20664-1 - Semiglobal solvability for classes of non singular vector fields
Grantee:Vinícius Novelli da Silva
Support type: Scholarships in Brazil - Master