Retratos de fase de uma família de sistemas quadráticos planares integráveis com duas parábolas invariantes
In this work we prove the Grobman-Hartman Theorem and the Local Stable Manifold Theorem, classical results in the study of the local behavior of the solutions of nonlinear differential equations. Then we provide the global phase portrait in the Poincaré disc of all quadratic planar differential syst...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Brasil |
| Institución: | Universidade Federal de Santa Maria (UFSM) |
| Repositorio: | Manancial - Repositório Digital da UFSM |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufsm.br:1/22160 |
| Acceso en línea: | http://repositorio.ufsm.br/handle/1/22160 |
| Access Level: | acceso abierto |
| Palabra clave: | Equações diferenciais ordinárias Teorema de Grobman-Hartman Teorema da variedade estável local Sistemas quadráticos planares Retratos de fase Parábolas invariantes Ordinary differential equations Grobman-Hartman theorem Local stable manifold theorem Quadratic planar system Phase portraits Invariant parabolas CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Sumario: | In this work we prove the Grobman-Hartman Theorem and the Local Stable Manifold Theorem, classical results in the study of the local behavior of the solutions of nonlinear differential equations. Then we provide the global phase portrait in the Poincaré disc of all quadratic planar differential systems with two invariant parabolas given by equations f1 = 0, f2 = 0 and a first integral of the form H = f 1 f 2 , where , are real constants. |
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