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| Author(s): |
Otavio Henrique Perez
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São José do Rio Preto. 2022-02-02. |
| Institution: | Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto |
| Defense date: | 2022-01-28 |
| Advisor: | Paulo Ricardo da Silva; Daniel Cantergiani Panazzolo |
| Abstract | |
The main object of study of this Thesis is a special class of differential equations called constrained differential systems (or impasse systems). This work is divided in two parts, and in each part we address two classical problems from ordinary differential equations. The first one concerns the study of singularities of constrained systems and the classification their of phase portraits. An algorithm of resolution of singularities for such class of systems is presented, and we use this theory in the topological classification of singularities. Classical results on topological classification of analytic vector fields are extended to the context of analytic constrained systems. The second part concerns the study of flows of three-dimensional polynomial vector fields on invariant algebraic surfaces. We prove that, for a certain class of surfaces, the flow can be described by a polynomial constrained system defined on the plane. Moreover, the singularities of the constrained system are deeply related to geometric properties of the surface, as well as the flow of the vector field. Well-known systems from applied sciences exemplify our results. (AU) | |
| FAPESP's process: | 16/22310-0 - Discontinuous foliations and impasses |
| Grantee: | Otavio Henrique Perez |
| Support Opportunities: | Scholarships in Brazil - Doctorate |