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An introduction to the Qualitative Theory of Ordinary Differential Equations

Grant number: 19/00028-9
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): April 01, 2019
Effective date (End): June 30, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Tiago de Carvalho
Grantee:Isadora Zanato Leite
Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
Associated research grant:13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM


Throughout this project we will study the qualitative theory of Ordinary Differential Equations (ODEs). This study will be implemented through analysis of the phase portraits, which will provide us qualitative/geometric information’s regarding the dynamic behavior of such systems. Then we will deal with the formal results regarding the qualitative theory of vector fields including: The Existence and Uniqueness Theorem, the Flow Box Theorem, Grobman-Hartman's Theorem and The Poincaré-Bendixson's Theorem.

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