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| Author(s): |
Vinícius Novelli da Silva
Total Authors: 1
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| 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: | 2020-02-21 |
| Examining board members: |
Paulo Leandro Dattori da Silva;
Alexandre Kirilov;
Gerson Petronilho;
Sergio Luis Zani
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| 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 Χ ⊂ Tm Χ 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 Opportunities: | Scholarships in Brazil - Master |